ENGINEERS'  POCKETBOOK 


OF 


REINFORCED  CONCRETE 


By 
E.  LEE  HEIDENREICH 

M.  Am.  Soc.  Test.  Mat.,  M.  W.  S.  E.,  M.  Am.  Inst.  Min.  Eng. 


SECOND  EDITION 


CHICAGO 

THE  MYRON  C.  CLARK  PUBLISHING  CO. 

LONDON 

E.  &  F.  N.  SPON,  Ltd..  57  Haymarket 
1915 


Copyright,    1908. 
Copyright,   1915. 

By 

The  Myron  C.   Clark  Publishing  Co. 


PREFACE  TO  FIRST  EDITION. 

For  the  past  fifteen  years  the  author  has  been  largely  occu- 
pied with  the  study,  exploitation  and  construction  qf  reinforced 
concrete,  and  during  this  time  has  collected  a  very  considerable 
amount  of  literature  as  well  as  personal  experience  in  the  sub- 
ject, some  of  which  in  a  more  or  less  concise  manner  is  laid  be- 
fore his  engineering  colleagues  in  this  "Engineers'  Pocketbook  of 
Reinforced  Concrete." 

For  a  person  occupied  and  making  his  living  as  an  engineer 
it  is  at  best  a  thankless  task  to  write  a  pocketbook  in  his  spare 
moments,  but  when  the  subject  is  so  comparatively  new  and 
where  such  wonderful  possibilities  for  additions  and  amend- 
ments are  confronting  one  it  is  almost  impossible  to  find  a  proper 
moment  when  the  book  may  be  considered  temporarily  finished. 

From  1899  when  the  author  wrote  his  first  booklet,  "Monier 
Constructions"  (published  1900),  reinforced  concrete  has  made 
such  gigantic  strides  forward,  that  it  has  entered  every  branch 
of  civil  engineering,  and  the  American  Society  for  Testing  Ma- 
terials in  conjunction  with  the  American  Society  of  Civil  Engi- 
neers through  a  Joint  Committee  for  Concrete  and  Reinforced 
Concrete,  of  which  the  author  is  a  member,  is  endeavoring  to 
standardize  specifications  and  to  recommend  factors  and  formu- 
las "required  in  the  design  of  structures  in  which  this  material 
is  used."  As  yet  this  committee  has  not  attained  results  further 
than  "a  knowledge  of  the  work  such  a  report  demands." 

Meanwhile  the  author  has  been  writing,  changing,  substitut- 
ing and  improving  the  book  for  upwards  of  eight  years  and 
finally  lets  go  of  it  for  his  own  peace  of  mind,  trusting  to  future 
opportunities  for  further  changes  and  amendments.  A  pocket- 
book  is  needed,  and  the  author  presents  this  one  for  what  as- 
sistance it  may  render  to  constructors  in  reinforced  concrete. 

The  author  wishes  to  express  his  appreciation  to  the  many 
engineers  and  authors,  from  whose  treatises  quotations  have  been 
made. 

1H 


314622 


iv  PREFACE  TO  FIRST  EDITION. 

"Le  Beton  Arme,"  by  Paul  Christophe;  "Ciment  Arme,"  by 
M.  M.  C.  Berger  and  V.  Guillerme;  "Beton  und  Eisen,"  by  Dr. 
F.  von  Emperger;  "Concrete,  Plain  and  Reinforced,"  by  Taylor 
&  Thompson;  "Concrete  and  Reinforced  Concrete  Construc- 
tion," by  Homer  A.  Reid;  "Reinforced  Concrete,"  by  Buel  & 
Hill;  "Walls-,  Bins  and  Grain  Elevators,"  by  Prof.  Milo  S.  Ket- 
chum ;  "Reinforced  Concrete  Bridges  and  Viaducts,"  by  John  Po- 
dolsky,  besides  works  by  Prof.  Arthur  N.  Talbot,  Prof.  Edwin 
Thacher,  Walter  W.  Colpitts,  C.  E.,  and  many  others,  have  been 
referred  to,  whose  names  have  been  acknowledged  in  footnotes 
without  intentionally  missing  any  one. 

A  number  of  manufacturing  establishments  have  courteously 
furnished  much  information  as  to  their  specialties  and  their  ad- 
dress or  place  of  business  has  been  given  for  reference. 

In  the  compilation  of  the  different  data,  in  calculations  or 
checking  of  the  many  tables,  in  the  research  for  information 
from  current  literature  on  the  subject,  both  in  Europe  and  in 
America,  the  author  has  been  most  ably  and  loyally  assisted 
by  Miss  Alice  Law,  Chicago,  for  whose  untiring  efforts  he 
hereby  expresses  his  thankful  appreciation. 

E.  LEE  HEIDENREICH. 

New  York,  December  1,  1908. 


PREFACE  TO   SECOND  EDITION 

As  suggested  in  the  preface  to  first  edition,  the  author 
has  trusted  to  future  opportunities  for  further  changes  and 
amendments, — and  will  probably  continue  to  do  so. 

While  the  intention  at  first  was  to  adopt  the  new  nota- 
tions proposed  in  the  Progress  Report  of  the  Joint  Com- 
mittee of  the  International  Society  for  Testing  Materials, 
the  author  has  decided  to  await  the  results  of  conferences 
between  the  Joint  Committee  and  the  Committee  on  Nota- 
tion's appointed  by  that  body. 

The  changes  and  additions  in  the  second  edition  have  been 
prompted  by  the  development  of  the  art  and  by  the  de- 
ficiencies discovered  in  the  first  issue.  Several  tables  have 
been  added,  such  as  are  in  daily  use  in  the  author's  office. 

Under  "Bridges"  some  valuable  information  has  been 
added,  adapted  from  "Designing  Methods,"  by  permission 
of  Mr.  Alfred  Lindau,  M.  Am.  Soc.  C.  E.,  of  the  Corrugated 
Bar  Company  of  Buffalo,  New  York,  and  as  in  the  first  edition 
the  author  has  acknowledged  the  sources  of  information  in 
footnotes  and  otherwise. 

The  author  begs  to  express  his  gratitude  to  his  col- 
leagues and  to  the  public  for  their  kind  reception  of  his 
earlier  endeavors  and  hopes  that  the  new  edition  wfll  be 
accepted  in  the  spirit  in  which  it  is  given — an  attempt  to 
produce  a  pocketbook  which,  in  a  measure,  follows  the 
improvements  in  the  art. 

E.    LEE    HEIDENREICH. 

Kansas   City,   Mo., 
January  1,  1915. 


TABLE   OF   CONTENTS. 

Page 

CHAPTER  I.— MATERIALS  AND  MACHINES  USED  IN  RE- 
INFORCED CONCRETE   CONSTRUCTION 1 

Definition  of  Reinforced  Concrete — Cement:  Portland  Ce- 
ment— Barrels  and  Sacks — Storage — Standard  Specifica- 
tions— Necessity  for  Tests  on  the  Work — Sampling  Cement 
for  Testing — Other  Tests — Aggregates:  Choice  of  Aggre- 
gates— Determination  of  Voids  in  Aggregates — Table  of 
Voids — Sand — Selection  of  Sand — Sand  for  Mortar — Sand 
for  Concrete — Table  of  Sand — Cleanness  of  Sand — Washing 
of  Sand — Voids  in  Sand — Weight  of  Sand — Standard  Sand — 
Screenings — Gravel — Choice  of  Crushed  Stone — Size  of 
Crushed  Stone — Crusher  Run — Rock  Crushers — Table  of 
Rock  Crushers — Voids  in  Graded  Mixtures — Voids  in  Loose 
Broken  Stone — Cinders — Mortar:  Strength  of  Mortar — Vol- 
ume of  Mortar  with  Varying  Proportions  of  Sand — Weight 
of  Mortar — Mortar  Tests — Retempered  Mortar — Concrete: 
Proportioning  Concrete — Usual  Methods  of  Proportioning 
Concrete — Fuller's  Rule — Thacher's  Table — Proportioning 
Concrete  for  Maximum  Strength — For  Maximum  Density — 
Concrete  in  Different  Classes  of  Work — Mixing — Mixtures, 
Wet  or  Dry — Mixtures  for  Plain  Concrete — For  Reinforced 
Concrete — The  Proper  Consistency — Hand  or  Machine  Mix- 
ing— Batch  or  Continuous  Mixers — Classification  of  Batch 
Mixers — Table  of  Batch  Mixers — Classification  of  Con- 
tinuous Mixers — Table  of  Continuous  Mixers — Hains  Grav- 
ity Mixer — Steel:  High  or  Low  Carbon — Medium  Steel — 
Percentage  of  Reinforcement — Mechanical  Bond — Rein- 
forcing Steel — Loose  Rods  for  Reinforcing — Square  Bars 
and  Round  Rods — Twisted  Bars — Corrugated  Bars — Dia- 
mond Bars — Thacher  Bars — Cup  Bars — Collings  Corru- 
gated Bars — Wire  Fabric — Triangle  Mesh  Reinforcement — 
Lock-Woven  Fabric — American  Wire  Fabric — Welded  Wire 
Fabric — Expanded  Metal — Kahn  Rib  Metal — Beam  and 
Girder  Units — Cummings  Girder  Frame — Pittsburgh  Steel 
Products  Co.'s  Beam  Reinforcement — Xpantrus  Bar — "Unit" 
Frame — Kahn  Trussed  Bar — Luten  Truss — Hooped  Column 
Reinforcement — Cummings  Hooped  Column — American 
•Hooped  Column — Smith  Hooped  Column — Structural  Steel — 
I-Beams — Channels — Angles — Table  of  Area  and  Circum- 
ference of  Circles — Table  of  Properties  of  Sections. 

vii 


viii  CONTENTS. 

Page 

CHAPTER   II.— DESIGN   AND    CONSTRUCTION   OF   BUILD- 
INGS     67 

General  Discussion:  General  Assumptions  Made  in  De- 
sign— Percentage  of  Steel  Reinforcement — Basis  of  Calcu- 
lations— Dead  Loads — Live  Loads — Allowable  Stresses — 
Bending  Moments  for  Beams — Bending  Moments  for 
Slabs — Cross  Reinforcement  in  Slabs — Shearing  Pro- 
visions— Location  of  Stirrups  in  Beams — Adhesion  of  Con- 
crete to  Steel — Modulus  of  Elasticity — Summary  of  Tal- 
bot's  Tests  on  Tee  Beams — Foundations:  Types  of  Founda- 
tions— Bearing  Power  of  Soils — Pile  Foundations — The 
Raymond  Pile — The  Simplex  Pile — The  Corrugated  Pile — 
The  Pedestal  Pile — The  Chenoweth  Pile — Other  Forms  of 
Piles — Pile  Driving — Slab  Foundations — Raft  Foundations 
— Portable  Foundations — Floors:  Floor  Loads — Factor  of 
Safety — Classification — Slab  Floors — Beam  Floors — Beam 
and  Tile  Floors — Arch  Floors — Manufactured  Floors — 
Floors  Without  Beams  or  Girders— Umbrella  Flat  Slab 
System — Heidenreich  Flat  Slab  System — Calculation  of 
Slabs — Straight-Line  Formula — Tables — Parabolic  Line 
Formula — Tables — Maximum  Bending  Moment  in  Slabs — 
Beams  and  Girders:  Loose  Rod  Systems — Frame  Systems — 
Tables  of  Safe  Loads  and  Steel  Areas  for  Beams — Tables  of 
Safe  Loads  and  Steel  Areas  for  Slabs — Formulas  Giving 
Ultimate  Strength  of  Beams:  Class  No.  1 — Class  No.  2 — 
Class  No.  3 — Tables — Columns:  Classification — Rectangular 
or  Polygonal  Columns — Hooped  Columns — Design  of  Hooped 
Columns — Tables — Considfire's  Formula — Tables  —  Euler's 
Formula — Structural  Details:  Roofs — Stairs — Structural  * 
Steel  or  Cast  Iron  Columns — Bracket  Connections — Example 
of  Building  Designed  According  to  the  Foregoing  Prin- 
ciples: Assumptions — Slabs — Beams — Girders — Location  of 
Stirrups — Wall  Girders — Roof  Slab — Roof  Beams  and  Roof 
Girders — Columns — Foundations — Raft  2-7 — Quadrilateral 
Raft  4-5-9-10 — Square  Footings  12,  13,  17  and  18 — Conclu- 
sion— Sequence  of  Operations  in  Construction:  Clearing  the 
Site — Lumber  and  Reinforcing  Materials — Placing  the  Re- 
inforcement— Making  Concrete — Delivering  Concrete — 
Depositing  Concrete — Concreting  Columns — Concreting. 
•Walls — Joining  Successive  Days'  Work — Protection  of  Con- 
crete in  Setting — Protection  Against  Freezing — Forms, 
Molds,  Centering  and  Falsework:  Kind  of  Lumber — Table 
of  Working  Stresses  in  Lumber — Points  to  Consider  in  the 
Design  of  Forms — Assumptions  Made  in  the  Design  of 
Forms — Fastening  of  Forms — Joints  in  Forms — Spacing  of 
Studs — Thickness  of  Lagging — Rotation  in  the  Use  of 


CONTENTS.  ix 


Forms  —  Alignment  and  Setting  of  Forms  —  Adhesion  of 
Concrete  to  Forms  —  Time  to  Remove  Forms  —  Column  and 
Floor  Forms  —  Forms  in  Combined  Steel  and  Concrete 
Construction  —  Separately  Molded  Members  —  Eliminating 
the  Use  of  Forms  —  Small  Tools  for  Mixing,  Conveying  and 
Ramming  —  Finishing  Concrete  Surfaces:  Types  of  Finish  — 
Hair  Cracks  —  Mortar  Facing  —  Using  Special  Dry  Mixture  — 
Bringing  Aggregates  into  Relief  —  Tooling  —  Plastering 
Concrete  —  Painting  and  Varnishing  —  Waterproofing: 
Waterproofing  Cracked  Walks  or  Joints  Between  Steel 
and  Concrete  —  Protection  of  Steel  to  Be  Ineased  in  Con- 
crete —  Coloring  Cement  Mortar. 

CHAPTER    III.—  THE     DESIGN    AND     CONSTRUCTION    OF 
BRIDGES     ...............................................  211 

Flat  Slab  and  Girder  Bridges  —  Classification  by  Load- 
ings: Class  No.  1  —  Class  No.  2  —  Class  N.o.  3—  Load  Dia- 
grams: Live  Loads:  Wheel  Loads  on  Roadway  —  Wheel 
Loads  on  Tracks  —  Impact  —  Treatment  of  Loads  for  Girder 
Bridges  —  Abutments  and  Side  Walls  —  Weights  and  Di- 
mensions of  Electric  Cars  —  Detailed  Design  of  a  Flat 
Slab  Bridge:  Problem  —  Dead  Load:  Live  Loads:  Road 
Roller:  Electric  Car  —  Transverse  Reinforcement  —  Shear- 
ing Investigation  —  Side  Walls  for  Retaining  Fill  —  Water- 
proofing —  Bearing  on  Abutments  —  Girder  Bridges:  Problem 
—  Floor  Slab  —  Design  of  Slab  —  Girders  —  Girder  Gl  — 

—  Shearing  Provisions  —  Girder   G2   —   Girder  G3  —  Live 
Loads  —  Shearing     Provisions  —  Stirrups  —  Bent     Up     Bars  — 
Girder  G2  —  Bearing  of  Bridge  on  Abutment  —  Tables  — 
Girder  Bridges:  Reinforcing  Steel  —  Tables  —  Current  Meth- 
ods: Parabolic  Arch  without  Hinges  —  Parabolic  Arch  with 
Two  Hinges  —  Flat  Parabolic  Arch  with  Two  Hinges  —  For 
3-Center  'Arch  —  For    5-Center   Arch  —  For    7-Center   Arch  — 
Classification    of    Arch    Bridges  —  The    Elastic    Theory    of 
Arches     Simplified:     Introduction  —  Reactions     Caused     by 
Concentrated  Load  —  Successive  Steps  in  the  Design  of  an 
Arch  —  Line     of     Pressure     Due     to     Dead     Load  —  Line     of 
Pressure    for    the    Critical    Condition    of   Loading  —  Critical 
Condition    of   Loading   for   a   Given    Section  —  Proof    of    the 
Correctness   of   Locating   Points   A   and   B  —  Approximate   An- 
alysis of   Dead   Load  —  Thickness   of   Arch   Ring  at   Crown 
and  Springing  —  Thickness  of  Arch  Ring  on  Both   Sides  of 
Crown   Down  to  the   Skewback  —  Location   of  Neutral  Axis 

—  Thermal  Stresses  —  Example  of  an  Arch  Designed  Accord- 
ing   to    the    Elastic    Theory:     Assumptions  —  Constructing 
the  A,rch  Ring  —  Dead  Load  Diagram  —  Live  Load  Diagram 


x  CONTENTS. 

Page 

— Maximum  Fiber  Stresses — Table  of  Dead  and  Live  Loads 
at  Joints  of  Arch — Moments,  Stresses,  etc.,  at  the  Crown — 
Moments,  Stresses,  etc.,  at  the  Springing — Moments, 
Stresses,  etc.,  at  Joint  4 — Construction  of  Arch  Center- 
ing— Examples  of  Centering  for  Two  50-Ft.  Arches — Cen- 
tering for  the  Pollasky  Bridge — Concreting  the  Arch — Re- 
moval of  Arch-Centering — Grand  River  Bridge,  Grand 
Rapids,  Mich. — The  Santa  Monica  Viaduct. 

CHAPTER   IV.— ABUTMENTS   AND   RETAINING  WALLS... 296 

Theories  for  Pressure  of  the  Filling:  Rankine's  Theory 
— Weyrauch's  Theory — Coulomb's  Theory — Cain's  Theory — 
Trautwine's  Theory — Rankine's  Formulas — Caine's  Formu- 
las— General  Discussion:  Thrust — Back  Filling — Drain- 
age— Expansion  Joints — Temperature  Cracks — Masonry 
Retaining  Wall:  Calculation  of  Resultant  Pressure — 
Stability  Against  Overturning — Stability  Against  Sliding 
— Stability  Against  Crushing — Reinforced  Concrete  Re- 
taining Wall  of  Beam  Type:  The  Vertical  Beam — Foun- 
dation— Reinforced  Concrete  Retaining  Wall  With  Count- 
erforts: Calculation  of  Pressure  P — Vertical  Walls — 
Counterforts — Foundation  —  Conclusion — Retaining  Wall 
Forms:  Setting  the  Forms — Removing  the  Forms — Ex- 
pansion Joints — Wall  Form  Tie — Examples  of  Construc- 
tion: Retaining  Walls,  Paris,  France — Retaining  Wall, 
Great  Northern  Ry.,  Wash. — Specifications  for  Reinforced 
Concrete  Retaining  Wall:  General — Workmanship — Re- 
inforcement— Loading  and  Risks — Measurement  and  Pay- 
ment. 

CHAPTER    V.— CULVERTS,     CONDUITS,     SEWERS,     PIPES, 

AND     DAMS 320 

Arch  Culverts:  Box  Culverts:  Assumptions — Design,  of 
Covers  for  Box  Culverts — Diagram  for  the  Design  of 
Covers  for  Box  Culverts — Design  of  Sides  of  Box  Cul- 
verts— Diagram  for  the  Design  of  Sides  of  Box  Culverts — 
Cost  of  Concrete  Culverts — Examples  of  Arch  Culverts: 
Standard  Arch  Culverts,  C.,  B.  &  Q.  R.  R. — Arch  Culvert, 
Kalamazoo,  Mich. — Arch  Culvert,  Great  Northern  Ry. — 
Examples  of  Box  Culverts:  Standard  Box  Culverts,  C., 
B.  &  Q.  R.  R. — Conduits,  Sewers  and  Pipes:  Erosive 
and  Transporting  Powers  of  Water — Resistance  of  Soil  to 
Erosion  by  Water — Kutter's  Formula — Table  of  Flow  of 
Water  in  Circular  Pipes — Grade  of  Sewers — Calculations — •• 
Calculation  for  Internal  Pressure — Calculation  for  Ex- 
ternal Pressure — Myer's  Formula — Talbot's  Formula — 
Rankine's  Rule — Reinforcement  for  Sewers — Thickness 


CONT-ENTS.  xi 

,  Page 

and  Weight  of  Reinforced  Concrete  Pipe — Stresses  In 
Pipes  and  Rings  According  to  Talbot's  Researches — Con- 
centrated Load — Distributed  Vertical  Load — Distributed 
Vertical  and  Horizontal  Load — Summary  of  Tests  Made  on 
Concrete  Pipes — Forms  for  Sewers — Dams:  Classification 
— Comparative  Features — Pressure  on  the  Immersed  Sur- 
face— Conclusion — Types  of  Construction — The  Open  Front 
Dam — The  Half  Apron  Dam — The  Curtain  Dam. 

CHAPTER   VI.— TANKS,    RESERVOIRS,    BINS    AND    GRAIN 

ELEVATORS    357 

Tanks  and  Reservoirs:  General  Discussion — Shape  or 
Form  of  Tanks  and  Reservoirs — Calculations — Table  Giv- 
ing Capacity  of  Tanks — Foundations — Tightness  of  Tanks 
— Reinforcement — Cost — Tank  for  Montgomery  Ward  & 
Co.,  Chicago  Heights,  111. — Tank  for  American  Steel  & 
Wire  Co.,  Cleveland,  O. — Forms  for  an  Intake  Tank — Bat- 
tery Tanks — Bins  and  Grain  Elevators:  Action  of  Grain 
Flowing  From  a  Bin— Bridging  Action  of  Grain  in  a 
Bin — Table  of  Grain  Pressure — Ratio  of  Grain  to  Liquid 
Bressure — Vertical  Pressure — Ratio  Between  Lateral  and 
Vertical  Pressure — The  Coefficient  of  Friction — Pressure 
of  Coal  in  Bins — Tables  of  Pressure  for  Bituminous  and 
Anthracite  Coal — Weight,  Angle  of  Repose  and  Angle  of 
Friction  of  Various  Materials — Capacity  of  Bins — Conclu- 
sions— Classification  of  Grain  Elevators — Comparative 
Cost  of  Timber  and  Reinforced  Concrete  Elevators — Ce- 
ment Storage  Tanks,  Illinois  Steel  Co.,  South  Chicago, 
111. — Canadian  Pacific  Grain  Elevator,  Port  Arthur,  Ont. 

CHAPTER  VII.— CHIMNEYS,  MISCELLANEOUS  DATA, 
COST  OF  KEEPING,  ESTIMATING,  SPECIFICATONS, 
ETC 390 

Chimneys:  Calculation — The  Core  Theory — Wind  Press- 
ure and  Velocity — Approximate  Method  of  Calculation- 
Example — Summary  of  Points  in  Design  of  Chimneys — 
Construction — Concrete  Chimneys — Horsepower  of  Chim- 
neys— Construction  of  Molds — The  Wiederholt  Concrete 
Steel  Chimney — Manufactured  Articles:  Inspection:  Prog- 
ress Reporting  and  Keeping  of  Costs:  Blank  Forms — 
Notes  on  Estimating:  Plant  Expense — Percentage  to  Al- 
low for  Profits — Accident  Insurance — Blank  Form  for 
Estimate  of  Building — General  Specifications  for  Rein- 
forced Concrete:  In  General — Cement — Sand — Gravel  or 
Stone — Proportion — Mixing — Placing — Reinforcement — Ex- 
pansion— Centering — Removal  of  Forms — Freezing  Weath- 
er— Protecting  Work — Fireproofing  Structural  Steel — Ce- 


xii  CONTENTS. 

Page 

ment  Finish — Stresses — Tests — Finally — Standard  Specifi- 
cations for  Cement:  Natural  Cement — Portland  Cement — 
Specific  Gravity — Fineness- — Time  of  Setting — Tensile 
Strength — Constancy  of  Volume — Sulphuric  Acid  and  Mag- 
nesia— Uniform  Tests  of  Cement:  Sampling — Chemical 
Analysis — Specific  Gravity — Fineness — Normal  Consistency 
— Standard  Sand — Mixing — Storage  of  Test  Pieces — Tensile 
Strength — Constancy  of  Volume — Miscellaneous  Informa- 
tion— Glossary  of  Terms  Used  in  Plain  and  Reinforced 
Concrete — Useful  Information. 
INDEX 433-439 


CHAPTER    I. 

MATERIALS     AND     MACHINES     USED      IN      REIN- 
FORCED   CONCRETE    CONSTRUCTION. 

Definition  of  Reinforced  Concrete. — This  material  is  a 
combination  of  concrete  and  steel,  so  united  that  the  con- 
crete takes  the  compression,  while  the  steel  takes  the  tension 
and  assists  in  the  resistance  to  shear.  When  reinforced 
concrete  first  appeared  in  America  it  was  known  as  armored 
concrete;  subsequent  names  applied  to  it  have  been  ferro- 
concrete, ferro-cement,  steel-concrete,  and  concrete-steel. 
At  the  present  time,  however,  the  term  preferred  by  the 
majority  of  engineers  and  designers  is  reinforced  concrete. 

CEMENT. 

Cement  used  in  construction  is  either  natural  cement  or 
Portland  cement.  Natural  cement  being  manufactured  in 
much  less  quantity,  and  being  of  inferior  strength  to 
Portland,  is  used  so  little  in  comparison  with  Portland 
cement  that  its  use  .will  be  disregarded  in  this  book. 

Portland  Cement. — The  definition  of  Portland  cement, 
recommended  by  the  committee  on  standard  specifications  for 
cement  of  the  American  Society  for  Testing  Materials,  is  "the 
finely  pulverized  product  resulting  from  the  calcination  to  in- 
cipient fusion  of  an  intimate  mixture  of  properly  proportioned 
argillaceous  and  calcareous  materials.  It  has  a  definite 
chemical  composition  varying  within  comparatively  nar- 
row limits."  This  definition  is  supported  by  the  American 
Association  of  Portland  Cement  Manufacturers,  so  that  we 
may  consider  Portland  cement  to  be  nominally  a  definite, 
uniform  product. 

Barrels  and  Sacks. — Cement  is  sent  from  the  mills  in 
barrels  or  sacks.  For  long  shipments  or  when  there  is  risk 
of  dampness,  barrels  are  used,  but  the  general  mode  of 

1 


.REINFORCED'  •  CONCRETE. 

transportation  is  in  sacks.  Portland  cement  barrels  of  dif- 
ferent manufacturers  vary  in  weight  and  capacity.  If  tightly 
packed,  a  barrel  of  Portland  cement  may  contain  only  3.5  cu. 
ft.  and  if  very  loosely  measured  the  volume  may  be  4.2  cu.  ft. 
or  more.  The  generally  accepted  standard  is  that  a  barrel 
of  Portland  cement  shall  weigh  380  Ibs.  net,  the  barrel  weigh- 
ing 20  Ibs.  more,  and  that'  it  shall  contain  4  cu.  ft.  of  cement 
measured  loose.  Four  bags  of  cement  are  always  assumed 
to  be  equivalent  to  a  barrel;  a  sack  of  cement  is  then  gen- 
erally assumed  to  weigh  95  Ibs.,  and  to  contain  1  cu.  ft.  of 
cement  measured  loose. 

Cement  sacks  are  made  of  either  cloth  or  paper,  cloth 
being  preferred,  as  paper  bags  are  easily  torn  in  handling, 
causing  waste  of  cement.  Cloth  bags  may  be  returned,  and 
will  be  re-purchased  by  the  manufacturer;  paper  bags  cannot 
be  returned. 

Storage. — Cement  should  be  stored  in  a  dry  place.  It  is 
insufficient  that  it  be  stored  out  of  the  rain;  storage  in  a 
damp  basement  will  soon  ruin  cement  by  caking  it,  and  it 
should  not  be  stored  upon  the  ground  in  wet  weather. 
Cement  should  be  rejected  which  has  been  wet,  and  caked 
into  hard  lumps.  On  large  works,  enough  cement  should  be 
stored  to  last  a  month,  in  order  that  tests  may  be  made,  un- 
less tests  are  made  in  the  warehouse  of  the  manufacturer. 
Cement  several  weeks  old  is  better  seasoned  than  that  which 
is  fresh  from  the  mill.  Well  seasoned  cement  may  be  lumpy 
but  the  lumps  are  easily  broken  with  the  fingers,  in  which 
case  the  cement  is  entirely  satisfactory. 

Standard  Specifications. — The  recommendations  of  the 
committee  on  standard  specifications  for  cement,  of  the 
American  Society  for  Testing  Materials,  have  been  adopted 
by  so  many  societies  and  companies  that  they  may  be  re- 
garded as  practically  the  standard  throughout  the  country. 
These  requirements  for  Portland  cement  are  set  forth  in  the 
recommendations  on  the  opposite  page. 

Necessity  for  Tests  on  the  Work. — The  manufacture  of 
Portland  cement  has  reached  such  uniformity  that  fairly 


MATERIALS  AND  MACHINES.  3 

identical  results  may  be  attained  by  using  any  one  of  a 
number  of  well  known  brands,  so  that  the  choice  of  any 
particular  brand  is  ruled  largely  by  other  considerations 
than  its  own  intrinsic  qualities.  Though  cement  direct  from 
the  mill  is  uniform  and  reliable,  it  may  not  remain  so,  and 
tests  on  the  work  are  therefore  necessary  to  determine  its 
genuineness,  and  whether  it  is  reasonably  sound,  the  sound- 
ness of  a  cement  being  a  quality  that  can  be  readily  affected 
by  improper  storage,  etc.  The  fact  that  cement  is  satisfactory 
when  tested  is  no  indication  that  it  will  continue  to  be, 
hence  cement  which  is  not  used  for  some  time  after  test, 
should  be  tested  again,  if  there  is  any  possibility  that  damp 
weather  or  other  factors  have  affected  its  soundness. 

AMERICAN    SOCIETY   FOR   TESTING   MATERIALS'    REQUIRE- 
MENTS   FOR   CEMENT. 

SPECIFIC    GRAVITY. 
Dried  at  100°   C ..not  less  than  3.1 

FINENESS. 

Passing  No.  100  sieve not  less  than  92%  by  weight 

Passing  No.  200  sieve not  less  than  75%  by  weight 

TIME    OF    SETTING. 

Initial  set in  not  less  than   30  minutes 

Hard  set In  not  less  than  1  hour  nor  more  than  10  hours 

TENSILE    STRENGTH,    NEAT. 
Age.  Strength. 

24   hours   in   moist  air 175  Ibs.  per  sq.  in. 

7  days  (1  day  in  moist  air,  6  days  in  water) . .  .500  Ibs.  per  sq.  in. 
28  days  (1  day  in  moist  air,  27  days  in  water).  .600  Ibs.  per  sq.  in. 
TENSILE  STRENGTH,  ONE  PART  CEMENT,  THREE  PARTS  SAND. 

7  days  (1  day  in  moist  air,  6  days  in  water) 200  Ibs. 

28  days  (1  day  in  moist  air,  27  days  in  water) 275  Ibs. 

CONSTANCY   OF   VOLUME. 

Pats,  neat,  about  3  inches  in  diameter,  one-half  inch  thick  at 
the  center,  tapering  to  a  thin  edge,  kept  in  moist  air  for  24  hours. 

(a)  A  pat  is   then  kept  in  air  at  normal  temperature  and  ob- 
served at  intervals  for  at  least  28  days. 

(b)  Another  pat  is  kept  in  water  maintained  as  near  70°   F.  as 
practicable,  and  observed  at  intervals  for  at  least  28  days. 

(c)  A  third  pat  is  exposed  in  any  convenient  way  in  an  atmos- 
phere of  steam,  above  boiling  water,  in  a  loosely  closed  vessel  for 
five   hours. 

These  pats  .shall  remain  firm  and  hard  and  show  no  signs  of 
distortion,    checking,    cracking   or   disintegrating. 

SULPHURIC    ACID    AND    MAGNESIA. 

Anhydrous  Sulphuric  Acid  (SO3) not  over  1.75  per  cent 

Magnesia  (MgO) not  over  4  per  cent 


I  REINFORCED   CONCRETE. 

Sampling  Cement  for  Testing. — The  best  sampler  to 
use  is  one  similar  to  a  sugar-sampler,  which  takes  a  small 
cylinder  of  the  material  from  the  surface  to  the  center  of 
the  bag.  Small  samples  should  be  taken  from  a  great 
number  of  bags  and  mixed.  This  gives  a  better  average 
indication  of  the  cement.  On  large  works  it  is  customary 
to  sample  every  tenth  bag.  The  cement  so  taken  for  testing 
purposes  should  be  kept  away  from  the  air  and  dampness 
till  made  into  paste,  as  otherwise  it  may  not  be  in  the 
same  condition  as  the  cement  in  the  bags. 

Other  Tests. — Setting  and  hardening  qualities  should  be 
noted  by  estimating  the  time  required  before  a  pressure  of 
the  thumb-nail  is  resisted  by  a  cement  pat.  This  point  is 
where  initial  set  ends  and  final  set  begins.  Such  tests 
should  agree  with  the  standard  tests  above.  The  color  and 
weight  of  dry  Portland  cement  are  no  indication  of  quality. 
Mr.  W.  Purves  Taylor,  in  "Practical  Cement  Testing,"  states 
that  cement  balls  made  for  tests  should  be  soft,  pliable,  and 
damp  on  the  surface,  and  should  not  feel  warm  at  the  end  of 
20  minutes.  Cement  failing  in  this  is  quick-setting.  Such 
cement  often  becomes  slow-setting  on  being  stored  a  month 
or  two.  Good  cement  should  have  a  uniform  color  when 
drying.  Yellowish  spots  indicate  poor  cement.  The  color  of 
cement  hardening  in  air  is  a  better  indication  than  when  hard- 
ening under  water.  The  quantity  of  cement  paste  obtained 
by  using  different  percentages  of  water  is  the  same,  per  given 
weight  of  cement,  provided  the  compacting  is  the  same. 
Neat  cement  tests  afford  more  information  as  regards  the 
properties  of  the  cement  itself,  than  as  regards  how  it  will 
behave  in  the  work;  to  get  practical  information  regarding 
this,  mortar  and  concrete  tests  are  necessary  as  the  testing 
of  the  aggregates  to  be  used  is  of  more  practical  value. 

AGGREGATES. 

The  aggregates  used  with  cement  in  the  formation  of 
concrete  are  generally  sand  or  stone  screenings  and  gravel 
or  crushed  stone. 


MATERIALS  AND  MACHINES.  5 

Choice  of  Aggregates. — In  general  it  may  be  said  that 
concrete  aggregates  should  be  chosen  which  will  undergo 
no  future  alterations,  either  disintegration  due  to  chemical 
changes,  or  breaking  of  particles  under  the  rammer,  due  to 
the  presence  of  cracks  or  bruises  received  at  the  crusher. 
Other  things  being  equal,  rounded  aggregates  give  greater 
density  and  a  lower  percentage  of  voids,  since  the  compact- 
ness increases  as  the  particles  become  more  rounded.  In 
all  cases  a  well  graded  aggregate  gives  the  best  results; 
this  means,  not  a  mixture  of  two  sizes  of  aggregate  only, 
but  a  uniform  gradation  from  the  finest  material  up  to  the 
coarsest  to  be  used.  This  will  be  further  discussed  under 
Concrete.  An  excess  of  medium  sized  particles  of  the  aggre- 
gate decreases  the  density  and  also  the  strength  of  mortar 
or  concrete.  The  shape  of  the  particles  of  aggregate  has 
little  effect  on  mortar,  except  as  to  density,  but  concrete  is 
affected  by  the  shape  of  the  particles,  especially  of  coarse 
aggregate. 

Determination  of  Voids  in  Aggregates. — While  not  suit- 
able for  laboratory  practice,  the  following  method  of  meas- 
uring voids  in  the  field  has  been  found  adequate:- 

Fill  a  vessel  of  known  capacity  with  the  material,  then 
pour  in  all  the  water  it  will  contain;  measure  the  volume  of 
the  water  and  divide  by  the  volume  of  the  vessel.  The 
quotient  expresses  the  percentage  of  voids.  Some  experi- 
menters start  with  the  material  wet;  others  begin  with  it 
dry.  The  dry  method  allows  a  little  larger  factor  of  safety. 

Table  of  Voids. — Table  I  gives  the  specific  gravity,  weight 
solid,  and  weight  loose,  of  aggregates  varying  from  a  specific 
gravity  of  1.0  to  3.5.  To  use  the  table,  suppose  an  aggre- 
gate, for  instance,  limestone  of  specific  gravity  2.6,  con- 
tains 52  per  cent  of  voids, — its  weight  per  cubic  yard  is  seen 
to  be  2,101  Ibs.  Or  suppose  an  aggregate  weighing  162  Ibs. 


REINFORCED    CONCRETE. 


per   cubic   foot   solid   is   found  to  weigh  2,625   Ibs.   per  cubic 
yard  when  crushed,  the  voids  are  seen  to  be  40  per  cent. 
TABLE  I. — PERCENTAGES  OF  VOIDS. 


Specific 

Solid  Weight 

Loose  weight  in  Ibs.  per  cubic  yard 
when  voids  are:  — 

Gravity 

In  Ibs.  per 
cubic  foot 

In  Ibs.  pel- 
cubic  yard 

30% 

32% 

34% 

36% 

38% 

40% 

1.0 

62.35 

1684 

1179 

1145 

1111 

1077 

1044 

1010 

2.0 

124.7 

3367 

2357 

2289 

2222 

2155 

2088 

2  020 

2.1 

130.9 

3536 

2475 

2404 

2333 

2263 

2192 

212] 

2.2 

137.2 

3704 

2593 

2519 

2445 

2370 

2296 

2222 

2.25 

140.3 

3788 

2652 

2576 

2500 

2424 

2349 

2273 

2.3 

143.4 

3872 

2711 

2633 

2556 

2478 

2401 

2323 

2.35 

146.5 

3956 

2769 

2690 

2611 

2532 

2453 

2374 

2.4 

149.7 

4041 

2828 

2748 

2667 

25SH6 

2505 

2424 

2.45 

152.8 

4125 

288V 

2805 

2722 

2640 

2557 

2475 

2.5 

155.9 

4209 

2946 

2862 

2778 

2694 

2610 

2525 

2.55 

159.0 

4293 

3005 

2919 

2833 

2748 

2662 

2576 

2.6 

162.1 

4377 

3064 

2977 

2889 

2801 

2714 

2626 

2.65 

165.2 

4462 

3123 

3034 

2945 

2855 

2766 

2677 

2.7 

168.4 

4546 

3182 

3091 

3000 

2909 

2818 

2727 

2.75 

171.5 

4630 

3241 

3148 

3056 

2963 

2871 

2778 

2.8 

174.6 

4714 

3300 

3206 

3111 

3017 

2933 

2828 

2.85 

177.7 

4798 

3359 

3263 

3167 

3071 

2975 

2879 

2.9 

180.9 

4882 

3418 

3320 

3222 

3125 

3027 

2929 

2.95 

183.9 

4967 

3477 

3377 

3278 

3179 

3079 

2980 

3.0 

187.1 

5051 

3536 

3434 

3333 

3232 

3131 

3030 

8.1 

193.3 

'  6219 

3653 

3549 

3445 

3340 

3236 

3131 

3.2 

199.5 

5387 

3771 

3663 

3556 

3448 

3340 

3232 

3.3 

205.8 

5556 

3889 

3778 

3667 

3556 

3445 

3333 

3.4 

212.0 

5724 

4007 

3892 

3778 

3663 

3549 

3435 

3.5 

218.3 

5893 

4125 

4007 

3889 

3771 

3653 

3536 

Sand. — In  order  to  distinguish  between  sand  and  gravel, 
an  arbitrary  line  must  be  drawn  between  the  two.  In  this 
work  sand,  except  when  referring  to  standard  sand,  will  refer 
to  all  particles  of  gravel  passing  a  No.  5  sieve  (having  open- 
ings 0.16  in.  wide).  This  is  sand  about  1/6  in.  in  diameter 
and  under,  and  is  practically  identical  with  the  French  limit 
suggested  by  Mr.  Feret. 

Selection  of  Sand. — The  proper  selection  of  sand  as  one 
of  the  aggregates  for  concrete  is  largely  a  matter  of  judg- 


MATERIALS  AND  MACHINES. 


ment,   as    often,   sands   differing  very   materially     in     phys- 
ical characteristics  will  make  equally  good  concrete.     Coarse 
TABLE  I.  (Continued.) — PERCENTAGES  OF  VOIDS. 


Loose  weight  in  Ibs.  per  cubic  yard 
when  voids  are:  — 

Specific 
Gravity 

42% 

44% 

46% 

48% 

50% 

52% 

54% 

56% 

976 

943 

909 

875 

842 

808 

774 

741 

1.0 

1953 

1886 

1818 

1751 

1684 

1616 

1549 

1482 

2.0 

2051 

1980 

1909 

1838 

1768 

1097 

1626 

1556 

2.1 

2148 

2074 

2000 

1926 

1852 

1778 

1704 

1630 

2.2 

2197 

2121 

2046 

1970 

1894 

1818 

1742 

1667 

2.25 

2246 

2  1  08 

2091 

2014 

1936 

1859 

1781 

1704 

2.3 

2295 

2216 

2136 

2057 

1978 

1899 

1820 

1741 

2.35 

2344 

2203 

2182 

2101 

2021 

1939 

1859 

1778 

2.4 

2392 

2310 

2227 

2145 

2063 

1980 

1897 

1815 

2.45 

2441 

2357 

2273 

2189 

2105 

2020 

1936 

1852, 

2.5 

2490 

2404 

2318 

2232 

2147 

2061 

1975 

1889 

2.55 

2539 

'  2451 

2364 

2276 

2189 

2101 

2014 

1926 

2.6 

2588 

2498 

2409 

2320 

2231 

2142 

2052 

1963 

2.C5 

2636 

2546 

2455 

2364 

2273 

2182 

2091 

2000 

2.7 

2685 

2593 

2500 

2408 

2315 

2222 

2030 

2037 

2.75 

2734 

2G40 

2546 

2451 

2357 

2263 

2168 

2074 

2.8 

2783 

2687 

2591 

2495 

2399 

2303 

2207 

2111 

2.85 

2832 

2734 

2636 

2539 

2441 

2344 

2246 

2148 

2.9 

2881 

2781 

2682 

2583 

2483 

2384 

2285 

2185 

2.95 

2929 

2828 

2727 

2626 

2525 

2424 

2323 

2222 

3.0 

3027 

2923 

2818 

2714 

2609 

2505 

2401 

2296 

3.1 

3125 

3017 

2909 

2801 

2694 

2586 

2478 

2371 

3.2 

3222 

3111 

3000 

2889 

2778 

2667 

2556 

2445 

3.3 

3320 

3206 

3091 

2977 

2862 

2748 

2633 

2519 

3.4 

3418 

3300 

3182 

3064 

2946 

2828 

2710 

2593 

3.5 

sand  is  generally  better  than  fine  sand;  a  coarse  grain  will 
have  a  smaller  surface  area  than  a  number  of  fine  grains  of 
equivalent  volume,  so  that  coarse  sand  will  be  better  coated 
than  fine,  with  the  same  quantity  of  cement.  For  general 
work,  a  mixed  sand  is  better  than  either,  because  of  a  better 
gradation  of  particles  and  a  consequent  lower  percentage 
of  voids. 

Sand  for  Mortar. — Coarse  sand  is  better  for  rich  mortars, 
and  fine  sand  is  better  for  lean  mortars.  Fine  sand  makes 
a  mortar  of  lower  density;  to  remedy  this  a  richer  mixture 


8  REINFORCED    CONCRETE. 

must  be  used.  Mr.  Feret's  rule  is  that  the  coarse  graina 
should  be  double  the  fine  grains,  including  the  cement.  Fine 
sand  may  produce  a  mortar  only  one-third  as  strong  as  spe- 
cially graded  sand  mixed  with  cement  in  the  same  propor- 
tions. 

Sand  for  Concrete. — Sand  for  concrete  requires  more  fine 
material  than  mortar  sand,  and  tests  indicate  that  the  best 
percentages  passing  a  No.  40  sieve  may  range  from  about 
18  per  cent  for  a  1-2-4  concrete  up  to  27  per  cent  for  a  1-4-8 
concrete.  For  water-tight  concrete,  even  a  larger  percent- 
age of  fine  grains  appears  to  be  beneficial.* 

Table  of  Sand. — Table  II  from  Gillette's  "Handbook  of 
Cost  Data"  gives  the  voids  in  sand  from  various  localities. 

Cleanness  of  Sand. — The  phrase,  "clean,  sharp  sand,"  for 
so  many  years  a  stereotyped  form  in  specifications,  is  now 
obsolete.  Sharpness  of  sand  is  of  little  value  except  when 
it  indicates  the  presence  of  silica.  Cleanness  of  sand  is  also 
disregarded  by  many  engineers,  who  permit  the  presence  of 
loam  or  clay;  the  quantity  allowed  is  from  2  to  10  per  cent, 
some  authorities  allowing  even  15  per  cent.f  The  author 
would  prefer  that  all  specifications  should  state  that  not  over 
5  per  cent  of  loam  or  clay  should  be  permitted  in  mortar  or 
concrete  for  reinforced  concrete  work,  as  these  impurities 
have  a  tendency  to  fill  the  small  voids,  preventing  the  cement 
from  flowing  in,  and  thereby  reducing  the  adhesion  between 
the  cement  and  the  aggregates,  or  the  cement  and  the  rein- 
forcement. The  permission  to  use  sand  with  a  small  per- 
centage of  impurities  is  apt  to  be  taken  advantage  of  in  a 
dangerous  manner,  for,  except  where  silica  is  present,  loam 
consists  largely  of  vegetable  mold,  which  should  be  guarded 
against. 

Washing  of  Sand. — When  sand  containing  loam  or  clay 
must  be  used,  the  impurities  should  be  washed  out.  This 


•Sand  for  Mortar  and  Concrete,  Sanford  E.  Thompson,  Bulletin 
No.  3,  American  Assoc.  Portland  Cement  Mfrs.,  Philadelphia. 

fFor  tests  with  sand  containing  loam  and  clay  see  Report,  Chief 
of  Engineers,  U.  S.  A.,  1896,  p.  2826  et  seq.,  and  1905,  p.  3001;  also 
C.  J.  Griesenauer,  Engineering  News,  April,  1904;  also  Chas.  E. 
Mills,  Proc.  Engineers'  Club  of  Philadelphia,  Pa.,  April,  1904. 


MATERIALS  AND  MACHINES.  < 

TABLE  II. — VOIDS  IN  SAND. 

Locality.                                  Authority.  Voids.  Remarks. 

Ohio  River W.  H.  Hall 31%  Washed 

Sandusky,  O C.  E.  Sherman 40%  Lake 

Franklin  Co.,  O C.  E.  Sherman.. . .  40%  Bank 

Sandusky  Bay,  O S.  B.  Newberry. .  .  32.3%  

St.  Louis,  Mo H.  H.  Henby 34  . 3%  Miss.  Rivei 

Sault  Ste.  Marie H.  von  Schon 41 . 7%  River 

Chicago,  111 H.  P.  Boardman.  .  34  to  40%  

Philadelphia,  Pa 39%  Del.  River 

Mass.  Coast 31  to  34%  

Boston,  Mass ....     Geo.  A.  Kimball.  .  33%  Clean 

Cow  Bay,  L.  I Myron  S.  Falk..  . .  40*%  

Little  Falls,  N,  t.  .                           W.  B.  Fuller 45 . 6%  

Canton,  111 G.  W.  Chandler. . .  30%  Clean 

can  be  done  by  pouring  the  sand  into  the  upper  end  of  an  in- 
clined tank  filled  with  water  and  having  a  small  gate  at  the 
lower  end,  which  permits  the  escape  of  the  clean  sand,  the 
overflow  of  the  water  carrying  away  the  dirt.  Sand  can  also 
be  washed  in  a  concrete  mixer. 

Voids  in  Sand. — The  more  rounded  the  grains  of  a  mixed 
granular  material,  the  lower  the  percentage  of  voids.  Nat- 
ural sand,  therefore,  with  rounded  grains,  gives  the  lowest 
percentage  of  voids  of  any  material  used  as  an  aggregate. 
Ground  quartz  (with  angular  grains)  comes  next,  then 
crushed  shells  (with  flat  grains)  and  finally  crushed  quartzite 
(with  laminated  grains).*  In  all  aggregates  except  sand  the 
moistening  of  the  material  decreases  the  percentage  of  voids. 
This  is  because  the  addition  of  water  destroys  in  part,  the 
arching  or  frictional  effect,  permitting  the  finer  material  to 
enter  the  voids  of  the  larger  material.  With  sand,  however, 
dampness  holds  the  particles  apart  and  increases  the  per- 
centage of  voids,  the  maximum  occurring  when  the  per- 
centage of  water  varies  from  5  to  8  per  cent.  The  addition  of 
more  water,  however,  decreases  the  voids  again,  to  practically 
the  same  as  contained  in  dry  sand.  The  following  tests  by 
Mr.  Wm.  B.  Fullerf  bear  out  the  above  statement,  whether 
the  sand  be  tested  loose  or  compact: 

*Mr.  Feret. 
tReid,  "Concrete  and  Reinforced  Concrete  Construction." 


10  REINFORCED    CONCRETE. 

Percentage  of  voids. 
Loose.     Compact. 

Dry    34 

6  per  cent  water   44 

Saturated    33  26.5 

Weight  of  Sand. — From  dealers'  catalogs,  bank  sand  is 
given  as  weighing  2,500  Ibs.  per  cu.  yd.,  and  Torpedo  sand, 
3,000  Ibs.  per  cu.  yd. 

Standard  Sand. — As  recommended  by  the  American  So- 
ciety for  Testing  Materials,  standard  sand  is  the  natural  sand 
from  Ottawa,  111.,  screened  to  pass  a  sieve  having  20  meshes 
per  linear  inch  and  retained  on  a  sieve  having  30  meshes  per 
linear  inch;  the  wires  to  have  diameters  of  0.0165  and  0.112 
in.,  respectively,  i.  e.,  half  the  width  of  the  opening  in  each 
case.  Sand  having  passed  the  No.  20  sieve  shall  be  consid- 
ered standard  when  not  more  than  1  per  cent  passes  a  No. 
30  sieve  after  one  minute  continuous  sifting  of  a  500  gram 
sample. 

Screenings.— Screenings  are  often  used  as  a  fine  aggregate 
in  place  of  sand.  In  using  screenings,  the  aggregates  should 
be  carefully  mixed  dry,  as  otherwise  the  fine  material  will 
collect  in  lumps  and  impair  the  uniformity  of  the  concrete. 
Under  similar  conditions,  sand  produces  a  denser  concrete 
than  screenings.* 

Gravel. — Many  engineers  have  a  decided  preference  for 
gravel  over  crushed  stone  as  an  aggregate.  Gravel  is 
thought  by  many  to  be  superior  to  crushed  stone  in  that  the 
well  rounded  pebbles,  worn  down  as  found  in  nature  are 
the  survival  of  the  best  parts  of  the  stone,  the  weaker  por- 
tions having  been  worn  away,  also  that  round  fragments 
offer  less  surface  to  be  coated,  thus  insuring  better  union 
with  the  mortar  and  giving  under  similar  conditions,  a  denser 
concrete  than  broken  stone.  The  exponents  of  crushed 
stone,  however,  maintain  that  the  rough  surfaces  and  the 
angularity  of  broken  fragments  insure  better  bonding  of 
the  concrete.  Practice  in  all  lines  of  work  has  demon- 
strated that  equally  good  concrete  can  be  made  with  either. 

*Fuller  and  Thompson,   Trans.  Am.  Soc.  C.  E,  1907. 


MATERIALS  AND  MACHINES.  11 

In  using  gravel,  that  containing  mud  or  gravel  cemented  in- 
to lumps  with  mud,  should  be  avoided. 

Choice  of  Crushed  Stone.— The  best  stone  for  crushing 
purposes  is  that  which  is  hard  and  tough,  breaking  into 
angular  fragments,  with  rather  rough  surfaces.  Stone  which 
breaks  more  easily  in  some  directions  than  others,  or 
exhibits  cleavage,  is  hard  to  tamp  compactly.  Mica  schist 
is  of  this  class,  and  should  be  avoided  for  reinforced  con- 
crete, though  it  is  allowable  for  massive  construction.  All 
things  considered,  trap  rock  makes  the  best  aggregate,  as  it 
is  tough,  hard,  bonds  well,  and  furnishes  a  concrete  of  great 
strength.  Crushed  granite  is  also  very  good,  unless  the 
fragments  are  bruised  in  the  crushing.  Limestone  is  by 
far  the  most  used,  though  when  subjected  to  great  heat, 
limestone  will  calcine  and  crumble.  Some  sandstones  are 
used  with  excellent  results,  though,  as  a  rule,  sandstones  are 
not  considered  strong  enough.  Stone  which  yields  a  great 
deal  of  fine  material  in  crushing  should  be  avoided  as  such 
stone  is  not  strong. 

Size  of  Crushed  Stone. — The  size  to  which  an  aggregate 
should  be  reduced  by  crushing  depends  upon  the  class  of 
structure  in  which  the  stone  is  to  be  used.  Since  the  largest 
stone  makes  the  densest,  and  also  the  strongest  concrete,  the 
largest  stone  should  be  used  that  is  consistent  with  proper 
placing,  taking  into  account  the  dimensions  of  the  mold,  and 
the  size  and  disposition  of  the  reinforcing  rods  or  wires. 

In  using  large  stone,  care  must  be  taken  to  prevent  it 
from  separating  from  the  concrete,  and  to  prevent  it  from 
moving  the  reinforcement  out  of  place.  Stone  for  reinforced 
concrete  varies  from  l/2  in.  to  V/2  ins.,  that  passing  a  ^-in. 
ring  or  mesh  being  most  common. 

The  following  tests  show  that  the  size  of  the  stone  influ- 
ences the  density:* 

*Fuller  and  Thompson,  Trans.  Am.  Soc.    C.  E.,  1907. 


12  REINFORCED    CONCRETE. 

Stone.  Density.  Ratio. 

2%  ins.  .847  1.00 

1       in.  .814                             .96 

V2  in.  .788                             .93 

Crusher  Run. — When  limestone  is  selected,  the  run  of  the 
crusher  is  often  used  for  the  entire  aggregate.  Unless  care 
is  exercised,  however,  the  true  run  of  the  crusher  will  not 
be  obtained,  for,  if  the  crushed  stone  is  poured  into  a  heap, 
a  separation  of  the  different  sizes  is  sure  to  occur,  in  a 
greater  or  a  less  degree.  To  prevent  this,  the  crushed  stone 
should  fall  directly  into  the  gage-box  from  the  crusher. 
Even  when  the  true  run  of  the  crusher  is  obtained,  it  is  evi- 
dent that  the  product  may  not  be  uniform.  Slight  variations 
in  the  hardness  or  texture  of  the  stone  may  produce  great 
variations  in  the  size  of  the  crushed  material,  the  percentage 
of  fine  particles,  etc.  A  more  accurate  method  is  to  screen 
out  the  fine  material  and  then  mix  in  the  required  propor- 
tions. 

Rock  Crushers. — A  great  number  of  rock  crushers  are  on 
the  market.  In  general,  it  may  be  said  that  the  same  crusher 
will  crush  different  aggregates  to  different  percentages  of 
voids,  and  that  the  capacity  of  the  machine  varies  with  many 
conditions.  It  is  well  known  that  the  efficiency  of  a  crusher 
is  higher  on  a  short  time  test  than  on  a  long  time  test,  and 
while  a  crusher  may  be  used  up  to  its  rated  capacity  for  an 
hour  or  for  a  day,  the  average  efficiency  for  a  month  will  be 
found  much  less  than  this,  usually  about  SO  per  cent  of  the 
rated  capacity.  On  one  well-known  work,  a  machine  that 
puts  out  175  cu.  yds.  per  day  of  10  hours,  averaged  65  cu.  yds. 
per  day,  when  the  monthly  output  was  taken  as  a  basis  for 
calculation,  this  variation  being  due,  not  to  the  machine,  but 
to  the  feeding  and  operating,  which  are  difficult  to  maintain 
uniformly  on  long  time  tests. 

Table  of  Rock  Crushers. — The  favorite  crusher  for  use  in 
concrete  work  is  the  gyratory  crusher.  Table  III  gives  di- 
mensions and  other  data  regarding  a  well  known  make. 


MATERIALS  AND  MACHINES. 


13 


TABLE  III.— GATES  ROCK  CRUSHERS,  STYLE  K. 
Allis-Chalmers  Co.,  Milwaukee. 


Dimen- 
sions of 
Each  Re- 
ceiving 
Opening, 
About 

Weight  of 
Breaker. 

Capacity  per  hour,  According 
to  Character  of  Rock,  in 
Tons  of  2,0001bs.,  to 
Pass  Through  a 
Ring  of  — 

Small- 
est 
size 
Prod- 
uct 

Driving  Pulley. 

IN 
ii 

o& 

W 

14  to  21 
22  to  80 
28  to  45 
50  to  75 

Dimen- 
sions 
in 
inches. 

Rev. 

per 
Min. 

Inches 

Lbs. 

H 

H 

2 

2i 

3 

3} 

4 
120 

Inches 

Sx  30 
10  x  38 
12x44 
14x52 

20900 
31200 
45500 
64800 

15 

20 
30 

25 
40 
50 

30 
50 
70 
80 

40 
60 
80 
90 

70 
90 
100 

H 
if 

2 
2} 

32x12 

36  x  14 
40  x  16 
44  x  18 

400 
375 
350 
350 

Voids  in  Graded  Mixtures. — It  is  well  known  that  differ- 
ent aggregates,  screened  so  that  the  same  proportions  are 
retained  on  the  same  screens,  will  contain  different  percent- 
ages of  voids.  This  is  due  to  the  fact  that  different  kinds 
of  rock  crush  into  fragments  of  different  degrees  of  regu- 
larity— some  breaking  cubically,  others  in  sharp,  angular  frag- 
ments, etc.  It  is  to  be  noted  that,  other  things  being  equal, 
gravel  contains  a  smaller  percentage  of  voids,  and  weighs 
more  per  unit  volume  than  crushed  stone,  which  is  equiva- 
lent to  saying  that  the  compactness  increases  as  the  particles 
become  more  rounded. 

Voids  in  Loose  Broken  Stone. — For  practical  work,  Table 
IV,  from  Gillette's  "Handbook  of  Cost  Data,"  gives  percent- 
ages of  voids  for  various  kinds  of  stone  from  a  number  of 
localities. 

Cinders. — Cinders  are  used  for  concrete  in  fireproonng 
work,  such  as  floors.  Such  concrete  is  porous,  and  therefore 
a  poor  conductor  of  heat  or  sound,  and  is  much  lighter  than 
stone  concrete,  as  it  weighs  about  112  to  120  Ibs.  per  cu.  ft., 
while  stone  concrete  weighs  about  150  Ibs.  per  cu.  ft.  Cinders 
for  fireproofing  work  should  be  chosen  carefully,  as  the 
presence  of  unburned  coal  will  render  such  concrete  the 


14 


REINFORCED    CONCRETE. 


TABLE  IV. — VOIDS  IN  LOOSE  BROKEN  STONE. 


Authority. 

Voids. 

% 

Remarks. 

Sabin  

49.0 
44.0 

Limestone,  crusher  run  after  screening  out 
i-in.  and  under. 
Limestone  (  1  part  screenings  mixed  with  6 

Wm.  M.  Black  
J.  J.  R.  Croes  
S.  B.  Newberry  

46.5 
47.5 
47.0 

parts  broken  stone). 
Screened  and  washed,  2  ins.  and  under. 
Gneiss,  after  screening  out  £-in.  and  under. 
Chiefly  about  egg  size. 

H.  P.  Boardman  
Wm.  H.  Hall...  '.'.'.'.'.'. 
Wm.  H.  Hall  

Wm.  B.  Fuller..  . 
Geo.  A.  Kimball  
Myron  -S.  Falk  
W   H    Henby 

39  to  42 
48  to  52 
48.0 

50.0 

47.6 
49.5 
48.0 
43  0 

Chicago  limestone,  crusher  run. 
screened  into  sizes. 
Green  River  limestone,  2|  ins.  and  smaller, 
dust  screened  out. 
Hudson  River  trap,  2£  ins.  and  smaller,  dust 
screened  out. 
New  Jersey  trap,  crusher  run,  J  to  2.1  in. 
Roxbury  conglomerate,  \  to  2%  ins. 
Limestone,  ^  to  3  ins. 
2  -in.  size. 

Feret  

46.0 
53.4 
51.7 
52.1 

"              1^-in.  size. 
Stone,   1  .6  to  2.4  ins. 
0  .  8  to  1  .  6  in. 
"         0.4  to  0.8  in. 

A.W.Dow  
Taylor  and(Thompson 

G  W  Chandler 

45.3 
45.3 
54.5 
54.5 
45.0 
51.2 
40  0 

Bluestone,  89%  being  1£  to  2J  ins. 
90%  being  J  to  H  in. 
Trap,  hard,  1  to  2i  ins. 
"       i  to  1  in. 
0  to  2J  ins. 
"    soft,     |  to  2  ins. 
Canton    111 

Emile  Low  

C  M  Saville  . 

39.0 
46  0 

Buffalo  limestone,  crusher  run,  dust  in. 
Crushed  cobblestone,  screened  into  sizes. 

least  fireproof,  whereas  it  is  supposed  to  be  the  most  fire- 
proof. Good  boiler  furnace  cinders  make  the  best  cinder 
concrete.  Cinders  should  be  well  wet  before  being  used  in 
concrete,  and  should  not  be  heavily  rammed,  as  the  cinders 
will  crush.  Being  porous  and  light  in  weight,  cinders  are 
not  as  strong  as  gravel  or  stone,  and  should  not  be  used 
where  strength  is  required,  nor  should  cinder  concrete  be 
subjected  to  load  before  one  month  old. 

When  slag  is  to  be  used  as  an  aggregate  it  should  be 
allowed  at  least  a  year  for  aeration  to  get  rid  of  the  sulphur, 
which  would  disintegrate  the  concrete.  Many  failures  have 
occurred  from  using  slag  not  sufficiently  aerated,  as  other- 
wise it  is  a  satisfactory  aggregate.* 


"Thomas  Potter,  Builders'  Journal,  London,  Dec.  5,  1906. 


MATERIALS  AND   MACHINES.  15 

MORTAR, 

Mortar  is  a  mixture  of  cement,  sand  or  screenings,  and 
water.  In  European  practice,  mortar  is  often  used  in  rein- 
forced concrete  construction.  American  practice  limits  the 
use  of  mortar  to  facing,  finishing,  etc.,  except  in  certain 
constructions,  such  as  chimneys  and  water-tight  receptacles. 

Strength  of  Mortar. — The  strength  of  mortar  depends 
upon  its  density  and  the  percentage  of  cement  it  contains. 
Evidently  a  change  of  density  must  be  accomplished  by  the 
sand,  since  there  is  practically  no  variation  in  different  ce- 
ments. -It  has  been  found  that  sands  with  rounded  grains 
contain  the  lowest  percentage  of  voids,  and  therefore  produce 
mortars  of  the  least  volume,  which  are  the  densest  and 
strongest  mortars.  Apparent  exceptions,  where  greater 
strength  is  obtained  by  using  broken  stone  screenings,  may 
be  caused  by  the  fine  particles  of  the  screenings  uniting  chem- 
ically with  the  cement.  Coarse  sand  gives  higher  strength 
than  fine  sand.  Mica,  when  laminated,  may  be  injurious, 
having  more  effect  upon  the  compressive  than  upon  the  ten-* 
sile  strength  of  mortar.  Mica  to  2  per  cent  is  unimportant. 

Volume  of  Mortar,  with  Varying  Proportions  of  Sand. — 
Table  V  is  compiled  from  experiments  made  by  Mr.  Edwin 
Thacher.  All  materials  were  measured  loose,  and  gently 
shaken  down.  One  barrel  of  cement  contained  4.12  cu. 
ft.  loose,  thus  requiring  6.56  barrels  per  cu.  yd.  One  volume 
of  Portland  cement  yielded  0.78  volumes  of  stiff  cement  paste 
on  the  addition  of  0.35  volumes  of  water.  The  sand  used 
was  moist,  ordinary  coarse  and  fine  mixed,  containing  38 
per  cent  of  voids. 

TABLE  V.— VOLUME  OP  MORTAR. 
Parts  of  sand  mixed  with 

1    part    of    cement 1.0  1.5  2.0  2.5      3.0      3.5      4.0      5.0 

Volume  of  slush   mortar..  1.40  1.78  2.17  2.55     2.98     3.39    3.82     4.65 
Required  for  1  cu.  yd. — 

Cement,  bbls 4.70  3.70  3.04  2.58     2.21     1.94     1.72     141 

Sand,    cu.   yds 0.71  0.84  0.92  0.98     1.01     1.03     1.05     1.08 

Volume     of     dry       facing 

mortar    (rammed)     1.22  1.57  1.93  2.28    2.64     2.99     3.35     4.08 

Required  for  1  cu.  yd. — 

Cement,   bbls 5.40  4.18  3.41  2.88     2.49     2.20     1.96     1.61 

Sand,   cu.   yds 0.82  0.95  1.04  1.10     1.14     1.17     1.20     1.23 


16 


REINFORCED   CONCRETE. 


Weight  of  Mortar. — From  experiments  by  Mr.  Feret,  it  is 
found  that  1-3  mortars  with  sand  of  fine,  medium  and  coarse 
grains  respectively,  weigh  approximately  the  same,  122  Ibs. 
per  cu.  ft.  If  the  three  sands  be  mixed  in  the  best  propor- 
tions, the  weight  of  the  mortar  reaches  141  Ibs.  per  cu.  ft., 
as  shown  in  Table  VI. 

Mortar  Tests. — Mortar  tests  on  the  work  are  receiving 
more  attention  than  formerly,  since  it  is  found  that  tests  in- 
volving the  aggregates  are  of  more  value  than  tests  of  the 
cement  alone.  Cement  is  generally  uniform  when  its  sound- 
ness has  been  established,  and  steel  for  reinforcement  is  also 
uniform  and  reliable,  but  concrete  aggregates  vary  consider- 
ably in  different  parts  of  the  country,  so  that  statements 
made  regarding  a  sand  in  one  locality  may  not  apply  to  that 
of  another.  Tests  of  cement  were  formerly  the  only  tests 
made.  Mortar  and  concrete  -tests  are  now  assuming  import- 
ance, and  in  all  municipal  work  the  tendency  is  to  secure 
a  maximum  density  of  the  aggregates  by  actual  tests  on  the 
•building  premises,  whereby  a  maximum  economy  may  be 
reached  simultaneously  with  maximum  strength. 

Retempered  Mortar. — Generally  speaking,  mortar  should 
not  be  used  after  it  has  attained  a  certain  set,  but  there  are 
instances  where  such  mortar  after  being  thoroughly  re- 
worked, preferably  without  adding  any  water,  can  be  used 
to  great  advantage  as  a  binder  between  old  and  new  work — 
for  instance,  in  repairing  concrete  sidewalks  where  the  finish 
has  scaled  off,  or  for  finishing  rough  surfaces. 

TABLE  VI. — WEIGHT  OP  MORTAR. 


1-3  Mortar 
by 
Weight 

Wt.  in  Ibs. 
per  cu.  ft. 

Density 

Voids 

Ratio  compressive 
strength  after  one  year 

In  fresh 
water 

In  air 

Coarse  Sand  

122 

.665 

.335 

.68 

.60 

Medium  Sand  

123 

.640 

.360 

.45 

.50 

Fine  Sand  

123 

.575 

.425 

.34 

.34 

Mixed  in  best  pro- 
portions   

141 

.  .734 

.266 

1.00 

1.00 

MATERIALS  AND  MACHINES.  17 

CONCRETE. 

Concrete  is  an  artificial  stone  composed  of  cement  with 
suitable  aggregates,  which  may  be  sand  and  gravel,  sand 
and  crushed  stone,  screenings  and  crushed  stone,  or  any 
other  combination  of  these  materials,  before  described. 

Proportioning  Concrete. — Many  of  the  usual  methods  of 
proportioning  concrete  are  unsatisfactory,  owing  to  the  fact 
that  the  laws  governing  the  mixing  and  setting  of  concrete 
are  net  definitely  understood.  A  number  of  formulas  and 
rules  have  been  devised  to  regulate  the  quantity  of  cement 
and  aggregates  to  use  per  cubic  yard  of  concrete.  The  usual 
field  practice  in  America  is  to  take  cement  and  aggregates  by 
volume;  in  France,  the  cement  is  measured  by  weight,  the 
aggregates  by  volume;  in  Germany  both  are  measured  by 
weight.  In  American  testing  laboratories,  the  practice  is  to 
measure  cement  and  aggregates  by  weight. 

Usual  Methods  of  Proportioning  Concrete. — Hitherto, 'the 
practice  has  been  to  mix  concrete  by  taking  1  part  cement 
with  certain  parts  of  sand  and  crushed  stone  or  gravel.  This 
practice  is  gradually  changing,  however,  in  view  of  the 
fact  that  the  best  concrete  is  that  in  which  the  aggregate 
is  uniformly  graded  from  coarse  to  fine.  Another  point  in 
favor  of  abandoning  the  former  method  is  that  the  1-2-3 
mixture  of  one  contractor  may  be  identical  with  the  1-3-5 
mixture  of  another,  owing  to  differences  in  the  sizes  of  sand 
and  stone.  In  view  of  this,  it  is  preferable  to  abandon  speci- 
fying mixtures  as  1-2-3,  1-2-4,  1-3-5,  but  as  1-5,  1-6,  1-8,  re- 
spectively, in  which  case  the  5,  the  6  or  the  8  parts  of  aggre- 
gate are  mixed  up,  reducing  the  voids  to  whatever  figure  is 
necessary  for  maximum  density,  and  then  the  cement  added. 
Both  methods  of  proportioning  will  be  considered,  since  both 
methods  are  in  use  at  the  present  time.  The  best  rules  gov- 
erning former  practice  are  given  below. 

Fuller's  Rule. — An  approximate  rule  for  ready  calculation 
is  the  one  originated  by  Mr.  Wm.  B.  Fuller,  and  is  as  fol- 
lows: Divide  11  by  the  sum  of  the  parts  (by  volume)  of  all 
the  ingredients;  the  quotient  is  the  number  of  barrels  of 


18  REINFORCED   CONCRETE. 

Portland  cement  required  per  cubic  yard  of  concrete.  Mul- 
tiplying this  by  the  number  of  parts  of  sand  and  of  stone 
will  give  the  number  of  barrels  of  each.  To  reduce  barrels 
to  cubic  yards,  multiply  by  0.14  (since  a  barrel  contains  3.8 
cu.  ft.  and  there  are  27  cu.  ft.  in  a  cubic  yard). 

For  example,  suppose  we  wish  to  mix  a  concrete  in  the 
proportion   1-3-6.     Then 


11'  H-  10  =1.1  barrels  of  cement  required  per  cubic  yard 
of  concrete. 

3  X  1-1  X  0.14  =  0.462  cu.  yds.  of  sand  required  per  cubic 
yard  of  concrete. 

6  X  1-1  X  0.14  =  0.924  cu.  yds.  of  crushed  stone  required 
per  cubic  yard  of  concrete. 

Fuller's  rule  gives  slightly  more  cement  per  cubic  yard 
than  is  given  in  Table  VII. 

Thacher's  Table.  —  Table  VII  is  compiled  from  experi- 
ments conducted  by  Mr.  Edwin  Thacher.  In  these  experi- 
ments, the  volumes  of  all  materials  were  measured  loose,  but 
gently  shaken  down.  A  barrel  of  cement  was  taken  at  4.1 
cu.  ft. 

Proportioning    Concrete    for    Maximum    Strength.  —  It    is 

well  known  that  with  any  given  sand  and  stone,  with  a  fixed 
quantity  of  cement,  the  mixture  that  gives  the  least  volume 
will  furnish  a  cement  of  maximum  strength.  Such  a  mixture 


MATERIALS  AND  MACHINES. 


19 


TABLE  VII. — PROPORTIONS  OF  MATERIALS  FOR  CONCRETE. 


Mir.tures. 

Required  for  one  cubic  yard  rammed  concrete. 

Stone,  1  in.  and 
und.,  dust 
screened  out. 
(46%  voids.) 

Stone,  2£  in  and 
und.,  dust 
screened  out. 
(41%  voids.) 

Stone,  2  2  in. 
with  most  small 
stone  scr'n'd  out 
(45%  voids.) 

Gravel,  f  in. 
and  under. 

§            rrt              ** 

1    1.0    2.C 
1       .026 
1       .0    3.0 
1       .0    3.6 

!i  u!  ft 

M                W 

g^        .>      a,  >> 

g2      *g  3        g  3 

|l  iM  ^ 

4       -o 

2.30    0.35    0.74 
2.10    0.32    0.80 
.89    0.29    0.86 
.71    0.26    0.91 

CJ          CO           02 

2.57    0.39    0.78 
2.29    0.35    0.70 
2.06    0.31    0.94 
1.84    0.28    0.98 

O          02          CO 

2.63    0.40    0.80 
2  34    0.36    0.89 
2.10    0.32    0.96 
1.88    0.29    1.00 

O          CO          02 

2.72    0.41    0.83 
2.41    0.37    0.92 
2.16    0.33    0.98 
1.88    0.29    1.05 

1       .5    2.5 
1       .5    3.0 
1       .5    3.5 
1       .5    4.0 
1       .5    4.5 

2.05    0.47    0.78 
1.85    0.42    0.84 
1.72    0.39    0.91 
1.57    0.36    0.96 
1.43    0.33    0.98 

2.09    0.48    0.80 
1.90    0.43    0.87 
1.74    0.40    0.93 
1.61    0.37    0.98 
1.46    0.33    1.00 

2.16    0.49    0.82 
1.96    0.45    0.89 
1.79    0.41    0.96 
1.64    0.38    1.00 
0.51    0.35    1.06 

.83    0.42    0.73 
.71    0.39    0.78 
.57    0.36    0.83 
.46    0.33    0,88 
1.34    0.31    0.91 

1    2.0    3.0 
1    2.0    3.5 
1    2.0    4.0 
1    2.0    4.5 
1    2.0    5.0 

1.70    0.52    0.77 
1.57    0.48    0.83 
1.46    0.44    0.89 
1.36    0.42    0.93 
1.27    0.39    0.97 

1.73    0.53    0.79 
1.61    0.49    0.85 
1.48    0.45    0.90 
1.38    0.42    0.95 
1.29    0.39    0.98 

1.78    0.54    0.81 
1.66    0.50    0.88 
1.53    0.47    0.93 
1.43    0.43    0.98 
1.33    0.39    1.03 

1.54    0.47    0.73 
1.44    0.44    0.77 
1.34    0.41    0.81 
1.26    0.38    0.86 
1.17    0.36    0.89 

1    2.5    3.5 
1    2.5    4.0 
1    2.5    4.5 
1    2.5    5.0 
1    2.5    5.5 
1    2.5    6.0 

1.45    0.55    0.77 
1.35    0.52    0.82 
1.27    0.48    0.87 
1.19    0.46    0.91 
1.13    0.43    0.94 
1.07    0.41    0.97 

1.48    0.56    0.79 
1.38    0.53    0.84 
1.29    0.49    0.88 
1.21    0.46    0.92 
1.15    0.44    0.96 
1.07    0.41    0.98 

1.51    0.58    0.81 
1.42    0.54    0.87 
1.33    0.51    0.91 
1.26    0.48    0.96 
1.18    0.44    0.99 
1.10    0.41    1.03 

1.32    0.50    0.70 
1.24    0.47    0.75 
1.16    0.44    0.80 
1.10    0.42    0.83 
1.03    0.39    0.86 
0.98    0.37    0.89 

1    3.0    4.0 
1    3.0    4.5 
1    3.0    5.0 
1    3.0    5.5 
1    3.0    6.0 
-1    3.0    6.5 
1    3.0    7.0 

1.26    0.58    0.77 
1.18    0.54    0.81 
1.11    0.51    0.85 
1.06    0.48    0.89 
1.01    0.46    0.92 
0.96    0  44    0.95 
0.91    0.42    0.97 

1.28    0.58    0.78 
1.20    0.55    0.82 
1.14    0.52    0.87 
1.07    0.49    0.90 
1.02    0.47    0.93 
0.98    0.44    0.98 
0.92    0.42    0.98 

1.32    0.60    0.80 
1.24    0.57    0.85 
1.17    0.54    0.89 
1.11    0.51    0.93 
1.06    0.48    0.97 
1.00    0.45    1.01 
0.94    0.42    1.05 

1.15    0.52    0.72 
1.09    0.50    0.75 
1.03    0.47    0.78 
0.97    0.44    0.81 
0.92    0.42    0.84 
0.88    0.40    0.87 
0.84    0.38    0.89 

1    3.5    5.0 
1    3.5    5.5 
1    3.5    6.0 
1    3.5    6.5 
1    3.5    7.0 
1    3.5    7.5 
1    3.5    8.0 

1.05    0.56    0.80 
1.00    0.53    0.84 
0.95    0.50    0.87 
0.92    0.49    0.91 
0.87    0.47    0.93 
0.84    0.45    0.96 
0.80    0.42    0.97 

1.07    0.57    0.82 
1.02    0.54    0.85 
0.97    0.51    0.89 
O.S3    0.49    0.92 
0.89    0.47    0.95 
0.86    0.45    0.98 
0.82    0.43    1.01 

1.11    0.59    0.85 
1.06    0.56    0.89 
1.00    0.53    0.92 
0.96    0.51    0.95 
0.91    0.49    0.98 
0.86    0.47    1.01 
0.81    0.45    1.04 

0.96    0.50    0.76 
0.92    0.48    0  78 
0.88    0.46    0.80 
0.83    0.44    0.82 
0.80    0.43    0.85 
0.76    0.41    0.87 
0.73    0.39    0.89 

1    4.0    6.0 
1    4.0    6.5 
1    4.0    7.0 
1    4.0    7.5 
1    4.0    8.0 
1    4.0    8.5 
1    4.0    9.0 

0.90    0.55    0.82 
0.87    0.53    0.85 
0.83    0.51    0.89 
0.80    0.49    0.91 
0.77    0.47    0.93 
0.74    0.45    0.95 
0  71    0.43    0.97 

0.92    0.56    0.84 
0.88    0.53    0.87 
0.84    0.51    0.90 
0.81    0.50    0.93 
0.78    0.48    0.95 
0.76    0.46    0.98 
0.73    0.44    1.01 

0.95    0.58    0.87 
0.91    0.55    0.90 
0.87    0.53    0.93 
0.84    0.51    0.96 
0.81    0.49    0.98 
0.78    0.47    1.01 
0.75    0.45    1.04 

0.83    0.51    0.77 
0.80    0.49    0.79 
0.77    0.47    0.81 
0.73    0.44    0.83 
0.71    0.43    0.86 
0.68    0.42    0.88 
0.65    0.40    0.89 

1    5.0   9.0 
1    5.0  10.0 

0  66    0.50   0.90 
0.62    0.47    0.95 

0.67    0.52    0.93 
0.63    0.48    0.96 

0.70    0.53    0.96 
0.65    0.50    1.00 

0.61    0.46    0.83 
0.57    0.43    0.87 

20  REINFORCED   CONCRETE. 

is  the  densest  obtainable  under  the  given  conditions,  and  is 
obtained  when  the  volume  of  cement,  sand  and  water  just 
fills  the  voids  in  the  stone.  The  density  of  concrete  has  been 
found  to  vary  considerably  by  varying  the  proportions  of  the 
aggregates. 

Proportioning  Concrete  for  Maximum  Density. — In  this 
connection  may  be  cited  the  field  method  devised  by  Mr. 
Wm.  B.  Fuller,  which  is  to  determine  the  maximum  density 
by  trial.  His  method  is  as  follows: 

"Procure  a  piece  of  steel  pipe  8  to  12  ins.  in  diameter  and  about 
a  foot  long  and  close  off  one  end,  also  obtain  an  accurate  weighing 
scale.  Weigh  out  any  proportions  selected  at  random,  of  cement, 
sand  and  stone,  and  of  such  quantity  as  will  fill  the  pipe  about 
three-quarters  full,  and  mix  thoroughly  with  water  on  an  im- 
pervious platform,  such  as  a  sheet  of  iron;  then,  standing  the  pipe 
on  end,  put  all  the  concrete  in  the  pipe,  tamping  it  thoroughly, 
and  when  all  is  in  measure  and  record  the  depth  of  the  concrete  in 
the  pipe.  Now  throw  this  concrete  away,  clean  the  pipe  and  tools 
and  make  up  another  batch  with  the  total  weight  of  cement,  sand 
and  stone  the  same  as  before,  but  with  the  proportions  of  the  sand 
to  the  stone  slightly  different.  Mix  and  place  as  before  and  meas- 
ure and  record  the  depth  in  the  pipe,  and  if  the  depth  in  the  pipe 
is  less  and  the  concrete  still  looks  nice  and  works  well,  this  is  a 
better  mixture  than  the  first.  Continue  trying  in  this  way  until 
the  proportion  has  been  found  which  will  give  the  least  depth  in 
the  pipe.  This  simply  shows  that  the  same  amount  of  material  is 
being  compacted  into  a  smaller  space  and  that  consequently  the 
concrete  is  more  dense.  Of  course,  exactly  similar  material  must 
be  used  as  is  to  be  used  en  the  work,  and  after  having  in  this 
way  decided  on  the  proportions  to  be  used  on  the  work  it  is  de- 
sirable to  make  such  trials  several  times  while  the  work  is  in 
progress,  to  be  sure  there  is  no  great  change  in  materials,  or,  if 
there  is  any  change,  to  determine  the  corresponding  change  in  the 
proportions. 

"The  above  described  method  of  obtaining  proportions  does  not 
take  very  much  time,  is  not  difficult,  and  a  little  trouble  taken  in 
this  way  will  often  be  productive  of  very  important  results  over 
the  guess  method  of  deciding  proportions  so  universally  prevalent. 

"A  person  interested  in  this  method  of  proportioning  will  find 
on  trial  that  other  sands  and  stones  available  in  the  vicinity  will 
give  other  depths  in  the  pipe,  and  it  is  probable  that  by  looking 
around  and  obtaining  the  best  available  materials  the  strength  of 
the  concrete  obtainable  will  be  very  materially  increased. 

"As  a  guide  to  obtaining  the  best  concrete,  the  proportion  of 
cement  remaining  the  same,  the  following  are  the  results  of  exten- 
sive tests: 

"The  stone  should  all  be  of  one  size  or  should  be  evenly  graded 
from  fine  to  coarse,  as  an  excessive  amount  of  the  fine  or  middle 
sizes  is  very  harmful  to  strength. 

"All  of  the  fine  material  smaller  in  diameter  than  one-tenth 
of  the  diameter  of  the  largest  stone  should  be  screened  out  from 
the  stone. 

"The  diameter  of  the  largest  grains  of  sand  should  not  exceed 
one-tenth  of  the  diameter  of  the  largest  stone. 


MATERIALS  AND  MACHINES.  21 


"The  coarser  the  stone  used  the  coarser  the  sand  must  be,  and 
the  stronger,  more  dense  and  watertight  the  properly  proportioned 
work  becomes. 

"When  small  stones  only  are  used  the  sand  must  be  fine  and  a 
larger  proportion  of  cement  must  be  used  to  obtain  equal  strength." 

A  set  of  test  beams  has  shown  the  following  decrease  in 
strength,  due  to  decrease  in  density: 

Modulus  of  Rupture. 

Proportions.  Lbs.  Sq.  In. 

1:2:6  319 

1:3:5  285 

1:4:4  209 

1:5:3  151 

1:6:2  102 

1:8:0  41 

By  inspecting  the  above  figures  it  is  seen  that  although  the 
amount  of  cement  in  each  of  the  above  beams  was  the  same 
(namely,  1-9  of  the  total  material),  some  of  the  beams  were 
over  700  per  cent  stronger  than  others.* 

Concrete  in  Different  Classes  of  Work. — By  properly  pro- 
portioning concrete,  a  great  saving  in  materials  can  be  effect- 
ed. Lean  mixtures  can  be  used  in  heavy  construction  where 
the  concrete  is  stressed  only  in  compression.  Also  the  rich- 
ness of  the  mixture  can  be  varied  in  different  parts  of  the 
same  structure,  according  to  the  nature  of  the  stress,  rein- 
forcement, etc. 

Mixing. — The  mixing  of  concrete  is  as  important  as  the 
choice  of  the  aggregates.  In  general,  it  may  be  said  that 
mixing  for  a  long  time  retards  setting  and  increases  strength 
and  bond  capacity.  Thorough  mixing  is  essential  in  order  to 
produce  a  coherent  and  uniform  concrete;  the  leaner  and 
dryer  the  mixture  the  more  mixing  is  required.  Some  con- 
structors mix  the  materials  dry  till  a  uniform  color  and  ap- 
pearance are  secured  before  the  water  is  added.  Others  put  in 
the  material  and  the  water  at  once.  Either  way  will  produce 
good  results  except  for  hand  mixing,  where  the  mixing  of 
the  materials  in  the  dry  state  is  the  general  practice. 

Mixtures,  Wet  or  Dry. — Dry  mixtures  are  of  advantage 
because  the  forms  need  not  be  as  tight,  but  more  mixing  of 
the  dry  materials  and  more  tamping  are  required.  Wet  mix- 


*William  B.  Fuller. 


22  REINFORCED    CONCRETE. 

tures  require  less  tamping,  but  the  forms  must  be  tighter. 
With  dry  mixtures  the  forms  may  be  removed  sooner,  and 
they  are  used  where  quick  set  and  quick  strength  are  re- 
quired. Mixtures  too  wet  will  separate  and  the  cement  will 
go  to  the  bottom.  Dry  mixtures  require  more  wetting  sub- 
sequent to  placing  than  wet  mixtures,  because,  to  set  prop- 
erly requires  a  certain  amount  of  water;  if  this  is  not  all 
supplied  in  the  mixing,  it  should  be  supplied  afterward. 
Whether  wet  or  dry  mixtures  are  used  depends  chiefly  upon 
the  temperature  and  the  class  of  work. 

Mixtures  for  Plain  Concrete. — For  plain  concrete,  the 
author  agrees  with  Mr.  H.  W.  Parkhurst,*  who  summarizes 
as  follows: 

A  medium  concrete  or  one  that  has  not  enough  surplus  water 
to  produce  quaking,  while  having  enough  to  permit  easy  and 
thorough  ramming,  is  the  most  desirable.  To  specify  that  the 
concrete  should  not  quake  in  the  barrow  nor  in  handling,  but 
when  heavily  rammed,  would  seem  about  right  for  regulating  the 
amount  of  water.  It  is  probably  safer  to  have  an  excess  of  water 
than  a  deficiency.  Above  all,  it  is  of  the  utmost  importance  that 
concrete  shall  be  thoroughly  consolidated  by  ramming.  If  too  wet, 
ramming  will  tend  to  separate  the  ingredients,  and  if  too  dry,  no 
reasonable  amount  of  ramming  will  fill  the  voids  with  mortar. 

Mixtures  for  Reinforced  Concrete. — Wet  mixtures  for 
reinforced  work  are  preferred  in  America,  though  no  hard 
and  fast  rule  can  be  laid  down  to  gage  the  proportion  of 
water. 

The  quantity  of  water  varies,  first,  with  the  temperature. 
During  hot  weather,  a  so-called  wet  mixture  is  used  to  best 
advantage,  so  as  to  allow  for  evaporation.  In  cold  weather, 
although  heated  water  and  heated  sand  may  be  used,  there  are 
more  chances  for  freezing  with  wet  than  with  dry  mixtures, 
therefore  a  dry  mixture  is  preferable. 

The  quantity  of  water  varies  also  with  the  form  and  size 
of  the  mold.  For  molds  of  small  dimensions,  more  water  is 
required  in  order  that  the  concrete  may  properly  enter  into 
all  corners  and  surround  the  reinforcement.  In  molds  of 
larger  dimensions,  the  concrete  can  be  more  readily  tamped. 


•Journal  of  the  Western  Society  of  Engineers,  Vol.  VII,  No.  3. 


MATERIALS  AND  MACHINES. 


23 


Other  considerations  influence  the  amount  of  water  used: 
rich  mixtures  require  more  water  than  lean  ones;  fine  sand 
requires  more  water  than  coarse;  some  crushed  stone  ab- 
sorbs more  water  than  others — and  again,  for  water  tanks, 
chimneys  or  manufactured  articles,  where  a  mixture  of  1-4 


Fig.   1.— McKelvey  Mixer. 

is  used — and  the  aggregate  generally  consists  of  a  very 
coarse  sand,  usually  a  very  dry,  hard  rammed  mixture  is 
used. 

A  wet  mix,  in  place  of  being  tamped,  is  spaded  or  stirred 
by  continuous  working  with  a  suitable  tool.  A  dry  mix  is 
spaded  only  around  the  edges  of  the  mold,  but  otherwise 


Fig.    2.— Smith   Mixer. 

tamped  until  a  moisture  appears  on  top  of  the  concrete. 
European  engineers  are  very  successful  with  dry  mixtures, 
but  their  success  is  due  to  the  fact  that  the  mixing  and  the 
placing  are  very  carefully  done.  Their  rule  is  to  mix  con- 
crete moist  enough  to  flow  between  the  reinforcing  members 


24 


REINFORCED   CONCRETE. 


and  coat  them  with  cement,  but  which  will  at  the  same  time 
stand  heavy  ramming. 

The  Proper  Consistency  for  Concrete. — This  important 
factor  is  a  matter  of  judgment  and  experience  on  the  part  of 
the  engineer  and  contractor  in  charge  and  changes  during  a 
day's  work  according  to  local  circumstances,  dimensions  of 
forms,  shape  of  reinforcement,  etc.  The  behavior  of  plastic 
concrete  as  it  comes  from  the  mixer,  and  especially  while 
being  tamped  into  place,  will  with  a  little  practice  enable 
one  to  judge  if  the  amount  of  water  is  correct. 

Hand  or  Machine  Mixing. — Machine  mixed  concrete  is 
superior  in  quality  and  generally  less  expensive  than  hand 


Fig.    3. — Chicago   Improved    Cube    Mixer. 

mixed.  Mixing  by  hand  is  employed  only  when  the  quantity 
is  small  or  when  machinery  is  unobtainable. 

Batch  or  Continuous  Mixers. — For  reinforced  concrete,  it 
has  been  conceded  that  batch  mixing  is  preferable.  In  cases 
of  very  heavy  construction,  such  as  sea  walls  and  break- 
waters, locks,  dams,  etc.,  continuous  mixers  are  used  to  ad- 
vantage. Continuous  mixing  is  cheaper  and  more  rapid  than 
batch  mixing. 

Classification  of  Batch  Mixers. — The  following  classifica- 
tion of  batch  mixers  is  made  by  Mr.  Clarence  Coleman:* 

(1)  Revolving  drum  or  cylinder  with  horizontal  axis, 
with  deflectors,  receiving  and  discharging  without  stopping, 
concrete  visible. 


*Engineering  News,  Aug.  27,   1903. 


MATERIALS  AND  MACHINES. 


25 


(2)  Revolving  drum   formed  with   two  cones,  with  hori- 
zontal   axis,    deflectors,    receiving    and    discharging    without 
stopping,  concrete  visible. 

(3)  Revolving  circular  pan  or  trough,  vertical  axis,  frame 
with  radial  arms,  receiving  and  discharging  without  stopping, 
concrete  visible. 

(4)  Horizontal    revolving    cylinder,    mixes    by    revolving 
about  axis,  stops  to  receive  and  discharge,  concrete  invisible. 

(5)  Horizontal    trough,     semi-cylindrical     cross-section, 
longitudinal   shaft  carrying  blades,  which  mix  the  material 
and   feed   it   toward   the   discharge   end,   receiving  and   dis- 
charging without  stopping,  concrete  visible. 


Fig.   4. — Ransome  Mixer. 

(6)  Cubical  box  revolving  about  horizontal  axis  passing 
through  two  diagonally  opposite  corners,  door  at  one  side, 
stops  to  receive  and  discharge,  concrete  not  visible. 

(7)  Same  as  above,  except  with  corners  through  which 
axis   passes   cut   away,   tilts   to  discharge,   receives   and  dis- 
charges without  stopping,  concrete  visible. 

Table  of  Batch  Mixers.— Table  VIII  gives  comparative 
sizes  and  capacities,  and  Figs.  1  to  4  illustrate  several  well 
known  batch  mixers.  As  in  the  case  of  rock  crushers,  how- 
ever, the  actual  output  which  may  be  relied  upon  in  long- 
time runs  will  average  much  lower  than  the  rated  capacity. 


26 


REINFORCED    CONCRETE. 


TABLE  VIII.— BATCH  MIXERS. 


McKelvey  Concrete  Machinery  Co., 
Cleveland,  O. 

Koehring  Mixer 
Koehring  Machine  Co.,  M 
Wis. 

ilwaukee, 

Catalog 
No. 

Size  of  Batch 
in  cu.  ft. 

Capacity, 
yds.  per  hr. 

Catalog 
No. 

Size  of  Batch 

in  cu.  ft. 

Capacity, 
yds,  per  hr. 

0 

? 

7 
8 
9 

27 
21 

m 

9 
4* 
3 

25 
18 
12 
7* 

43* 

0—  B 
1—  B 
2—  B 
3—  B 

7 
11 
22 
27 

7 
14 
25 
30 

Chicago  Cube  Mixer. 
Municipal  Engineering  &  Contracting 
Co.,  Chicago. 

Polygon  Mixer. 
Waterloo  Cement  Machinery 
Waterloo,  la. 

Co., 

"Handy" 
6 
11 
17 
22 
33 
64 

« 

6 
11 
17 
22 
33 
64 

5} 
13 
24 
40 
50 
70 
120 

4 
5 
6 

7 

6 
10 
12 
16 

Per  day  of 
lOhrs. 
60 
100 
130 
180 

Ransome  Concrete  Machinery  Co., 
New  York. 

Smith  Mixer. 
The  T.  L.  Smith  Co.,  Chicago. 

1 

2 
3 
4 

10 
20 
30 
40 

10 
20 
30 
40 

Catalog 
No. 

Mixed 
dry. 

Volume 
unmixed. 

Yds. 
1  per  hr. 

R.  Z.  Snell  Manufacturing  Co., 
South  Bend,  Ind. 

0 
1 

2 

\l 

5 

6 
9 

m 

16} 

22 
30 

8| 

13 
20 

24* 
34i 
46 

9 
20 
30 
39 
46 
62 

0 

1 
2 
3 

3 
7 
11 
24 

I1 

8 
20 

Cropp  Mixer. 
A-.  J.  Cropp,  Chicago. 

Chicago  Concrete  Machinery  Co., 
Chicago. 

0 
1 

2 
3 

7  to  8 
10 
13 
16 
20 

15 
20 
25 
30 
40 

00 
0 
1 
2 

3J 
6 
9 
18 

5 
8} 
13 
26 

8 
14 
21 
42 

MATERIALS  AND  MACHINES. 


27 


Classification  of  Continuous  Mixers. — They  are  classified 
as  follows  by  Mr.  Clarence  Coleman:* 

(1)  Inclined  chute  fitted  with  pins,  material  slides  down 
by  gravity,  concrete  visible. 

(2)  Series  of  funnels  placed  one  above  another,  contain- 
ing baffles,  concrete  falls  by  gravity,  invisible  for  most  part. 

TABLE  IX. — CONTINUOUS  MIXERS. 


Scheiffler  Mixer. 
The  Hartwick  Machinery  Co., 
Jackson,  Mich. 

Drake  Mixer. 
Drake  Standard  Machine  Works, 
Chicago. 

Catalog  No. 

Capacity  per  hour  in 
cu.  yds. 

Catalog  No. 

Capacity  per  hour  in 
cu.  yds. 

2 

I* 

12  to  15 

1 
2 
3 
4 

4  Special 

P 

40 
20 
15 
7.5 
10 
2.5 

Eureka  Mixer. 
Eureka  Machine  Co.,  Lansing,  Mich. 

Foote  Mixer. 
W.  H.  Wilcox  Co.,  Binghamton,  N.  \  '. 

81 
82 
83 
84 
25 
23 

10  to  12 
10  to  18 
10  to  18 
10  to  18 
10  to  18 
2  to  4 

1 

2 

I 

6 
7 
12 

16 
U5 

Advance    Mixer. 
Cement  Machinery  Co.,  Jackson,  Mich. 

25  to  75 

on 


(3)  Long   inclined   box   of    square   section,    revolving 
horizontal  axis,  concrete  practically  invisible. 

(4)  Like    (3),    except    being   cylindrical,    with    deflectors. 
Practically  invisible. 


*Engineering-  News,  Aug.  27,  1903. 


28  REINFORCED    CONCRETE, 

(5)  Open  trough  or  closed  cylinder,  fitted  with  shaft  on 
which  are  paddles  or  blades  which  mix  and  feed  concrete 
toward  discharge  end,  concrete  visible. 

Table  of  Continuous  Mixers. — Table  IX  gives  compara- 
tive outputs  of  several  well  known  continuous  mixers. 

Hains  Gravity  Mixer. — The  Hains  Concrete  Mixer  Co. 
of  Washington,  D.  C,  manufacture  the  mixer  shown  in  Fig. 
5.  The  charge  passes  successively  through  the  hoppers. 


Fig.    5.— Hains  Gravity  Mixer,  Fixed  Hopper  Form. 

The  four  hoppers  at  the  top  have  a  combined  capacity  of 
one  of  the  lower  hoppers.  Each  top  hopper  is  charged  with 
cement,  sand  and  stone  in  the  order  named  and  in  the  proper 
proportions.  Water  is  then  dashed  over  the  tops  of  the 
rilled  hoppers  and  they  are  dumped  simultaneously  into  the 
hopper  next  below.  This  hopper  is  then  discharged  into  the 
next  and  so  on  to  the  bottom.  Meanwhile  the  four  top  hop- 
pers have  been  charged  with  materials  for  another  batch.  It 


MATERIALS  AND  MACHINES.  29 

will  be  observed  that  (1)  the  concrete  is  mixed  in  separate 
batches,  and  (2)  the  ingredients  making  a  batch  are  accurate- 
ly proportioned  and  begin  to  be  mixed  at  once  for  the  whole 
batch.  The  best  arrangement  is  to  have  the  top  of  the 
hopper  tower  carry  sand  and  stone  bins  which  chute  directly 
into  the  top  hoppers. 

STEEL. 

While  in  Europe  wrought  iron  is  preferred  for  reinforce- 
ment, steel  is  used  exclusively  in  the  United  States,  both  on 
account  of  lesser  cost  and  on  account  of  having  more  suitable 
qualities. 

High  or  Low  Carbon. — Engineers  differ  as  to  the  qualities 
of  steel  desirable  for  reinforcement,  some  apprehension  be- 
ing entertained  as  to  the  brittleness  of  certain  kinds  of  high 
carbon  steel. 

Open-hearth  steel  is  decidedly  preferable.  High  steel 
should  have  an  ultimate  strength  of  about  85,000  Ibs.  per  sq. 
in.,  with  an  elastic  limit  averaging  54,000  Ibs.,.  with  not  more 
than  0.067  per  cent  of  phosphorus,  0.06  per  cent  of  sulphur 
and  between  0.4  and  0.8  per  cent  of  manganese,  with  0.5  to 
0.6  per  cent  of  carbon,  and  showing  10  per  cent  elongation  in 
8  ins.  for  a  test  piece  ^  to  34  m-  m  diameter,  and  a  l/2  in. 
test  piece  should  bend  cold  110°  around  twice  its  diameter 
without  fracture. 

Low  carbon  steel  or  soft  steel  should  have  an  ultimate 
strength  of  from  54,000  to  62,000  Ibs.  per  sq.  in.,  with  an 
elastic  limit  not  less  than  one-half  the  ultimate  'strength.  It 
should  elongate  25  per  cent  in  8  ins.  and  bend  cold  180° 
double  without  fracture  on  outside  of  bend. 

Drawn  steel  wire  of  an  ultimate  strength  of  156,000  Ibs. 
per  sq.  in.  has  been  used,  with  an  elastic  limit  of  from  90,000 
to  126,000  Ibs.  in  wire  fabric  and  has  shown  many  remarka- 
ble results. 

For  a  medium  steel  of  32,000  to  35,000  Ibs.  elastic  limit  it 
is  customary  to  specify  a.  safe  strength  of  16,000  Ibs.  How- 
ever, for  steel  wire  of  90..000  to  126,000  Ibs.  the  author  has 


30  REINFORCED    CONCRETE. 

never  specified  more  than  30,000  Ibs.  as  safe  strength,  owing 
to  accidental  defects  by  indentation  in  handling. 

Owing  to  the  fact  that  the  coefficients  of  elasticity  of 
high  and  low  steel  are  very  nearly  equal,  and  hence  the  limit 
stretch  only  varies  as  0.001  of  the  length  for  soft  steel  to 
0.00167  of  the  length  for  high  steel — and  furthermore  since, 
according  to  Prof.  A.  N.  Talbot,  the  maximum  allowable 
stretch  of  concrete  lies  near  the  point  0.001,  it  would  appear 
that  nothing  could  be  gained  by  using  a  high  carbon  steel.* 
However,  the  author  has  since  found  that  by  using  a  high 
class  concrete,  of  proportions  such  as  1  cement  to  3  or  4  of 
aggregates  proportioned  for  maximum  density,  far  better 
results  were  obtained  using  high  carbon  steel  than  low  car- 
bon, and  owing  to  lesser  dimensions,  a  lower  dead  weight 
of  floor  slabs  and  girders  has  resulted,  showing  economy  in 
spite  of  the  fact  that  more  expensive  mixtures  of  the  con- 
crete were  used,  while  taking  advantage  of  the  properties  of 
high  carbon  steel. 

Medium  Steel. —  When  medium  steel  is  used  it  should 
have  an  ultimate  strength  of  from  60,000  to  68,000  Ibs.  per 
sq.  in.,  with  an  elastic  limit  of  not  less  than  one-half  the 
ultimate  strength.  It  should  elongate  22  per  cent  in  8  ins., 
and  bend  cold  180°  around  a  diameter  equal  to  the  thickness 
of  the  test  piece  without  fracture  on  outside  of  bend. 

In  the  above  bending  tests  for  soft  and  medium  steel  the 
quality  of  metal  should  be  such  that  it  will  stand  the  above 
described  tests  upon  a  test  piece  at  least  5/16  in.  in  diame- 
ter, after  being  heated  to  a  cherry  red  and  cooled  in  water  to 
a  temperature  of  70°  F. 

In  reinforced  concrete  permissible  working  stresses  are 
not  based  upon  the  ultimate  strength  of  the  steel,  but  upon 
the  elastic  limit,  owing  to  the  necessary  adhesion  between 
the  concrete  and  the  steel,  which  is  apt  to  be  destroyed  by 
any  reduction  in  the  sectional  area  of  the  steel,  such  as  oc- 
curs during  the  rapid  elongation  beyond  the  elastic  limit. 


*These  conclusions  were  based  upon  extensive  experiments 
made  by  Profs.  Talbot,  Hatt  and  Turneaure  with  concrete  mix- 
tures of  1-2-4  and  1-3-6. 


MATERIALS  AND  MACHINES. 


31 


Percentage  of  Reinforcement.— With  low  carbon  steel  the 
percentage  of  reinforcement  is  from  1  to  1.4  per  cent.  With 
high  carbon  steel,  the  figures  vary  from  0.7  to  0.9  per  cent 

TABLE  X. — WEIGHTS  OF  SQUARE  AND  ROUND  RODS. 

Calculated  for  steel,  weighing  489.6  Ibs.  per  cu.  ft. 
For  iron,  weighing  480  Ibs.  per  cu.  ft.,  substract  2%. 


Thickness 
or  diameter 
in  ins. 

Wt.  of 
•  Bar  in 

Ibs.  per  ft. 

Wt.  of 
•  Rod  in 
Ibs.  per  foot. 

Area  of 
•  Bar 
in  sq.  ins. 

Area  of 
•  Rod 
in  sq.  ins. 

Circumfer- 
ence of  ORod 
in  ins. 

A 

.003 

.003 

.001 

.0008 

.0982 

ft 

.013 

.010 

.0039 

.0031 

.1964 

s 

.030 

.023 

.0088 

.0069 

.2945 

1 

.053 

.042 

.0156 

.0123 

.3927 

& 

.083 

.065 

.0244 

.0192 

.4909 

I 

.119 
.163 

.094 
.128 

.0352 
.0479 

.0276 
.0376 

.5891 
.6872 

1 

.212 

.167 

.0625 

.0491 

.7854 

i 

.269 

.211 

.0791 

.0621 

.8836 

T5B 

.333 

.261 

.0977 

.0767 

.9818 

II 

.402 

.316 

.1182 

.0928 

1.0799 

§ 

.478 

.376 

.1406 

.1104 

1.1781 

a 

.561 

.441 

.1650 

.1296 

1.2763 

?B 

.651 

.511 

.1914 

.1503 

1.3745 

II 

.747 

.587 

.2197 

.1726 

1.4726 

* 

.850 

.668 

.2500 

.1963 

1.5708 

ft 

.960 

.754 

.2822 

.2217 

1.6690 

A 

.076 
.199 

.845 
.941 

.3164 
.3525 

.2485 
.2769 

1.7672 
1.8653 

f 

.328 

.043 

.3906 

.3068 

1.9635 

it 

.464 

.150 

.4307 

.3382 

2.0617 

if 

.607 

.262 

.4727 

.3712 

2.1599 

y 

1.756 

.380 

.5166  . 

.4057 

2.2580 

i 

1.913 

.502 

.5625 

.4418 

2.3562 

it 

2.075 

.630 

.6103 

.4794 

2.4544 

T8 

2.245 

1.763 

.6602 

.5185 

2.5526 

B 

2.420 

1.901 

.7119 

.5591 

2.6507 

i 

2.603 

2.044 

.7656 

.6013 

2.7489 

it 

2.793 

2.193 

.8213 

.6450 

2.8471 

H 

2.988 

2.347 

.8789 

.6903 

2.9453 

B 

3.1-91 

2.506 

.9385 

.7371 

3.0434 

of  the  cross  section;  thus  it  is  seen  that  by  using  high  car- 
bon steel,  there  is  only  required  from  0.64  to  0.7  as  much  re- 
inforcing steel. 


32 


REINFORCED    CONCRETE. 


Mechanical   Bond. — Mechanical   bond  is   obtained  by   de- 
formed rods,  supplementary  rods,  stirrups  or  anchors.     Such 
bond  is  absolutely  necessary  where  a  lean  concrete  is  used, 
in  which  the  adhesion  between  steel  and  concrete  has  a  low 
TABLE  X.  (Continued).— WEIGHTS  OF  SQUARE  AND  ROUND  RODS. 


Thickness 
or  diameter 
in  ins. 

Wt.  of 
•  Bar  in 
Ibs.  per  ft. 

Wt.  of 
•  Rod  in 
Ibs.  per  foot. 

Area  of 
•  Bar 
in  sq.  ins. 

Area  of 
•  Rod 
in  sq.  ins. 

Circumfer- 
ence of  ORod 
in  ins. 

1 

3.400 

2.670 

.0000 

.7854 

3.1416 

1C 

3.838 

3.015 

.1289 

.8866 

3.3380 

t 

4.303 

3.380 

.2656 

.9940 

3.5343 

4.795 

3.766 

.4102 

1.1075 

3.7306 

1 

5.312 

4.172 

.5625 

1.2272 

3.9270 

4 

5.857 

4.600 

.7227 

1.3530 

4.1234 

t 

6.428 

5.049 

.8906 

1.4849 

4.3197 

7 

n 

7.026 

5.518 

2.0664 

1.6230 

4.5161 

i 

7.650 

6.008 

2.2500 

1.7671 

4.7124 

A 

8.301 

6.519 

2.4414 

-    1.9175 

4.9088 

T 

8.978 

7.051 

2.6406 

2.0739 

5.1051 

9.682 

7.604 

2.8477 

2.2365 

5.3015 

1 

10.404 

8.178 

3.0625 

2.4053 

5.4978 

Vs 

11.169 

8.773 

3.2852 

2.5802 

5.6942 

l 

11.953 

9.388 

3.5156 

2.7612 

5.8905 

n 

12.763 

10.024 

3.7539 

2.9483 

6.0869 

2 

13.60 

10.68 

4.0000 

3.1416 

6.2832 

TB 

14.46 

11.36 

4.2539 

3.3410 

6.4796 

? 

15.35 

12.06 

4.5156 

3.5466 

6.6759 

A 

16.27 

12.78 

•   4.7852 

3.7583 

6.8723 

i 

'    17.21 

13.52 

5.0625 

3.9761 

7.0686 

18.18 

14.28 

5.3477 

4.2000 

7.2650 

19.18 

15.06 

5.6406 

4.4301 

7.4613 

20.20 

15.87 

5.9414 

4.6664 

7.6577 

1 

21.25 

16.69 

6.2500 

4.9087 

7.8540 

TR 

22.33 

17.53 

6.5664 

5.1573 

8.0504 

I 

23.43 

18.40 

6.8906 

5.4119 

8.2467 

tt 

24.56 

19.29 

7.2227 

5.6727 

8.4431 

i 

25.71 

20.19 

7.5625 

5.9396 

8.6394 

y 

26.90 

21.12 

7.9102 

6.2126 

8.8358 

i 

28.10 

22.07 

8.2656 

6.4918 

9.0321 

*i 

29.34 

23.04 

8.6289 

6.7771 

9.2285 

3 

30.60 

24.03 

9.0000 

7.0686 

9.4248 

value.  Mechanical  bond  caused  by  deforming  the  bars,  is  always 
preferable;  besides,  plain  and  deformed  bars  may  now  be  ob- 
tained in  the  market  at  the  same*price.  See  page  35. 


MATERIALS  AND   MACHINES. 


33 


Reinforcing   Steel. — There   are   a    great   many   styles   and 

TABLE  XI. — AREAS  OF  FLAT  ROLLED  STEEL. 
For  thicknesses,  from  T'g  in.  co  1  in.,  and  widths  from  1  in.  to  4  in. 


Thickness 
in  Ins. 

\" 

\" 

r 

1" 

H" 

ir 

1|" 

2" 

A 

.016 

.031 

.047 

.063 

.078 

.094 

.109 

.125 

f 

.031 

.063 

.094 

.125 

.156 

.188 

.219 

.250 

•j3B 

.047 

.091 

.141 

.188 

.234 

.281 

.328 

.375 

i 

.063 

.125 

.188 

.250 

.313 

.375 

.438 

.500 

T83 

.078 

.156 

.234 

.313 

.391 

.469 

.547 

.625 

i 

.094 

.188 

.281 

.375 

.469 

.563 

.656 

.750 

T75 

.109 

.219 

.328 

.438 

.547 

.656 

.766 

.875 

i 

.125 

.250 

.375 

.500 

.625 

.750 

.875 

1.00 

A 

.141 

,281 

.422 

.563 

.703 

.844 

.984 

.13 

1 

.156 

.313 

.469 

.625 

.781 

.938 

1.09 

.25 

u 

.172 

.344 

.516 

.688 

.859 

.03 

1.20 

.38 

i 

.188 

.375 

.563 

.750 

.938 

.13 

1.31 

.60 

b 

.203 

.406 

.609 

.813 

1.02 

.22 

1.42 

.63 

i 

.219 

.438 

.656 

.875 

1.09 

.31 

1.53 

.75 

•$ 

.234 

.469 

.703 

.938 

1.17 

.41 

1.64 

1.88 

1 

.250 

.500 

.750 

1.000 

1.25 

.50 

1.75 

2.00 

TABLE  XII. — WEIGHTS  OF  FLAT  ROLLED  STEEL,  PER  LINEAL  FOOT. 
One  cubic  foot  weighing  489.6  pounds. 


Thickness 
in  Ins. 

Y 

r 

f" 

1" 

H" 

li" 

If 

2" 

rV 

.053 

.106 

.159 

.213 

.266 

.319 

.372 

.425 

| 

.106 

.213 

.319 

.425 

.531 

.638 

.744 

.850 

I3B 

.159 

.319 

.478 

.638 

.797 

.956 

1.12 

1.28 

i 

.213 

.425 

.638 

.850 

1.06 

1.28 

1.49 

1.70 

.266 

.531 

.797 

1.06 

1.33 

1.59 

1.86 

2.12 

.319 

.638 

.956 

1.28 

1.59 

1.91 

2.23 

2.55    . 

. 

.372 

.744 

1.12 

1.49 

1.86 

2.23 

2.60 

2.98 

i 

.425 

.850 

1.28 

1.70 

2.13 

2.55 

2.98 

3.40 

„ 

.478 

.956 

1.43 

1.91 

2.39 

2.87 

3.35 

3.83 

1 

.531 

1.06 

1.59 

2.13 

2.66 

3.19 

3.72 

4.25 

1.1 

.584 

1.17 

1.75 

2.34 

2.92 

3.51 

4.09 

4.68 

1 

.638 

1.28 

1.91 

2.55 

3.19 

3.83 

4.46 

5.10 

H 

.691 

1.38 

2.07 

2.76 

3.45 

4.14 

4.83 

5.53 

Ks 

.744 

1.49 

2.23 

2.98 

3.72 

4.46 

5.21 

5.95 

H 

.797 

1.59 

2.39 

3.19 

3.98 

4.78 

5.58 

G.38 

l 

.850 

1.70 

2.55 

3.40 

4.25 

5.10 

5.95 

6.80 

34 


REINFORCED    CONCRETE. 


kinds  of  steel  in  use  for  reinforcing  concrete,  which  may  be 
classified  as  loose  rods,  expanded  metal,  fabrics,  beam  and 
girder  units,  column  reinforcements,  and  structural  steel. 

TABLE  XI.     (Continued). — AREAS  OP  FLAT  ROLLED  STEEL. 
For  thicknesses,  from  T*ff  in.  to  1  in.,  and  widths  from  {  in.  to  4  in. 


Thickness 
in  Ins. 

21" 

21" 

2J" 

3" 

3J" 

3J" 

3}" 

4* 

A 

.141 

.156 

.172 

.188 

.203 

.219 

.234 

.250 

i 

.281 

.313 

.344 

.375 

.406 

.438 

.469 

.500 

n 

.422 

.469 

.516 

.563 

.609 

.656 

.703 

.750 

J 

.563 

.625 

.688 

.750 

.813 

.875 

.938 

1.00 

6a 

.703 

.781 

.859 

.938 

1.02 

1.09 

1.17 

1.25 

1 

.844 

.938 

1.03 

1.13 

1.22 

1.31 

1.41 

1.50 

1 

.984 

1.09 

1.20 

1.31 

1.42 

1.53 

1.64 

1.75 

i 

.    1.13 

1.25 

1.38 

1.50 

1.63 

1.75 

1.88 

2.00 

I95 

1.27 

1.41 

1.55 

1.69 

1.83 

1.97 

2.11 

2.25 

f 

1.41 

1.56 

1.72 

1.88 

2.03 

2.19 

2.34 

2.50 

y 

1.55 

1.72 

1.89 

2.06 

2.23 

2.41 

2.58 

2.75 

¥ 

1.69 

1.88 

2.06 

2.25 

2.44 

2.63 

2.81 

3.00 

la 

1.83 

2.03 

2.23 

2.44 

2.64 

2.84 

3.05 

3  25 

v 

1.97 

2.19 

2.41 

2.63 

2.84 

3.06 

3.28 

3.50 

2.11 

2.34 

2.58 

2.81 

3.05 

3.28 

3.52 

3.75 

I3 

2.25 

2.50 

2.75 

3.00 

3.25 

3.50 

3.75 

4.00- 

TABLE  XII.     (Continued). — WEIGHTS  OP  FLAT  ROLLED  STEEL. 
One  cubic  foot  weighing  489.6  pounds. 


Thickness 
in  Ins. 

21" 

21" 

2f 

3" 

31" 

31" 

3J" 

4" 

A 

.478 

.531 

.584 

.638 

.691 

.744 

.797 

.850 

X 

.956 

1.06 

1.17 

1.28 

1.38 

1.49 

1.59 

1.70 

•fit 

1.43 

1.59 

1.75 

1.91 

2.07 

2.23 

2.39 

2.55 

i 

1.91 

2.13 

2.34 

2.56 

2.76 

2.98 

3.19 

3.40 

T*B 

2.39 

2.66 

2.92 

3.19 

3.45 

3.72 

3.98 

4.25 

I 

2.87 
3.35 

3.19 
3.72 

3.51 
4.09 

3.83 
4.46 

4.14 
4.83 

4.46 
5.21 

4.78 
5.58 

5.10 
5.95 

J 

3.83 

4.25 

4.68 

5.10 

5.53 

5.95 

6.38 

6.80 

X 

4.30 

4.78 

5.26 

5.74 

6.22 

6.69 

7.17 

7.65 

I 

4.78 

5.31 

5.84 

6.38 

6.91 

7.44 

7.97 

8.50 

tt 

5.26 

5.84 

6.43 

7.02 

7.60 

8.18 

8.76 

9.35 

¥ 

5.74 

6.38 

7.02 

7.65 

8.29 

8.93 

9.57 

10.20 

6.22 

6.91 

7.60 

8.29 

8.98 

9.67 

10.36 

11.05 

6.69 

7.44 

8.18 

8.93 

9.67 

10.41 

11.16 

11.90 

7.17 

7.97 

8.76 

9.57 

10.36 

11.16 

11.95 

12.75 

i5 

7.65 

8.50 

9.35 

10.20 

11.05 

11.90 

12.75 

13.60 

MATERIALS  AND  MACHINES.  35 

Loose  Rods  for  Reinforcing. — These  comprise  round  rods, 
square  and  flat  bars,  and  the  various  patented  deformed  bars. 
Owing  to  the  fact  that  in  the  United  States  nearly  all  the 
building  regulations  or  ordinances  require  a  mechanical 
bond,  and  specify  or  permit  such  concrete  mixtures  as  will 
require  it,  tables  are  here  inserted  showing  the  properties  of 
several  of  the  most  popular  forms  of  reinforcement  based 
upon  the  principle  of  mechanical  bond. 

There  are  a  number  of  prominent  systems  of  construc- 
tion that  are  built  up  of  loose  rods,  the  assembling  being 
done  in  the  field.  Practically  all  reinforced  concrete  work 
abroad  comes  under  this  classification,  and  formerly,  loose 
rod  systems  were  the  only  ones  used  in  America.  If  loose 
rods  are  used  for  reinforcing  instead  of  built  up  units,  great- 
er freedom  is  allowed  in  adapting  the  reinforcing  material  to 
the  part  of  the  structure  in  which  it  is  located.  A  number  of 
prominent  systems  of  reinforcement  which  are  built  of  loose 
rods,  will  be  given  further  on. 

Square  Bars  and  Round  Rods. — The  first  form  of  rein- 
forcing steel  to  be  used  was  plain  round  rods,  and  these  at 
first  found  favor  among  engineers  on  account  of  being 
more  easily  obtained  and  cheaper. 

However,  with  the  rapid  increase  in  the  demand  for 
efficient  reinforcement  the  manufacture  of  so-called  de- 
formed bars  developed  as  a  specialty  and  today  such  bars 
may  be  obtained  as  easily  and  as  cheaply  as  the  plain  product 
— and  should  therefore  always  be  preferred. 

Weights  and  Areas  of  Twisted  Bars.— Twisted  bars,  Fig. 
6,  are  not  covered  by  patent  and  can  be  obtained  in  open 
market.  These  bars  are  square  in  section,  so  that,  for  a 
given  thickness,  the  weights  and  areas  correspond  with  those 
for  plain  square  bars.  Table  XIII,  for  twisted  bars,  is  based 
upon  steel  weighing  489.6  Ibs.  per  cu.  ft. 


36 


REINFORCED    CONCRETE. 


Fig.  6.— Twisted  Bar. 

TABLE  XIII. — WEIGHTS  AND  AREAS  OF  TWISTED 
BARS. 


Thickness  of 
section  in  ins. 

Weight  in  Ibs. 
per  ft. 

Area  of  section 
in  sq.  ins. 

H 

0.212 

0.063 

3A 

0.478 

0.141 

H 

0.85 

0.25 

H 

1.32 

0.391 

U 

1.91 

0.563 

y* 

2.60 

0.765 

i 

3.4 

1.000 

IK 

4.3 

1.266 

IM 

5.3 

1.563 

Weights  and  Areas  of  Corrugated  Bars. — Xew  style  cor- 
rugated  bars,    Figs.   7   and   7-A   are   patented,   and   can   be   ob- 


Fig.   7. — Corrugated  Rounds — Type  C. 

TABLE  XIV.— SIZES  AND  WEIGHTS  FOR  TYPE  C. 


Size. 


Net  Section.      Weight  per  Ft. 


%" 

.110" 

.38  lb. 

7»" 

.190" 

.66  lb. 

% 

.250" 

.86  lb. 

% 

.300" 

1  05  Ibs. 

.440" 

1.52  Ibs. 

% 

.600" 

2.06  Ibs. 

1 

.780" 

2.69  Ibs. 

iH 

.990" 

3.41  Ibs. 

iS 

1.220" 

4.21  Ibs. 

MATERIALS  AND  MACHINES. 


37 


tained   from   the   Corrugated   Bar   Company,    Buffalo,    N.  Y. 

The  universal  corrugated  bar  shown   by  Fig.  8  is  made  by 

the    same    firm,    its    dimensions,    area,    etc.,    are    shown  by 
Table  XV. 


Figr.    7 -A. — Corrugated   Squares — Type  D. 
TABLE  XIV-A. — AREAS  AND  WEIGHTS  FOR  TYPE  D. 


Size. 

Net  Section. 

Weight  per  Ft. 

l/4" 

.060" 

.22  Ib. 

H* 

.140" 

.49  Ib. 

W 

.250" 

.86  Ib. 

w 

.390" 

1.35  Ibs. 

\" 

.56c" 

1.941bs. 

y& 

.76Q" 

2.64  Ibs. 

i  " 

l.OOa" 

3.43  Ibs, 

1/8" 

1.250" 

4.34  Ibs. 

IX* 

1.550" 

5.35  Ibs. 

38 


REINFORCED    CONCRETE. 


Fig.   8.— Universal  Corrugated  Bar. 


TABLE  XV.— WEIGHTS  AND  AREAS  OF  UNIVERSAL 
CORRUGATED  BARS. 


No. 

Size. 

Net  section 

Wt.  in  Ibs. 

in   sq.  ins. 

per  ft. 

1 

Jx  1 

0.19 

0.73 

2 
3 
4 
5 

6 

fell 
11  J1 

1  x2£ 

0.32 
0.41 
0.54 
0.65 
0.80 

1.18 
1.35 
1.97 
2.27 
2.85 

Weights    and   Areas    of   Diamond    Bars. — Diamond   bars, 
Fig,  9,  are  patented  and  can  be  obtained  from  the  Concrete 


Fig.  9.— Diamond  Bar. 


TABLE  XVI. — WEIGHTS  AND  AREAS  OF  DIAMOND 
BARS. 


Size 
in  ins. 

Weight  in  Ibs. 
per  ft. 

Area  of  section 
in  sq.  ins. 

1 
li 

.85 
1.33 
1.91 
2.60 
3.40 
5.31 

.25 
.39 
.56 
.76 
1.00 
1.56 

MATERIALS  AND  MACHINES.  39 

Steel  Engineering  Company,  New  York  City,  Their  sectional 
areas  and  weights  correspond  with  standard  sizes  of  square 
bars,  and  are  shown  in  Table  XVI. 

However,  according  to  Bulletin  No.  71,  "Tests  of  Bond  Be- 
tween Concrete  and  Steel,"  compiled  by  Prof.  A.  N.  Talbot  of 
the  University  of  Illinois  and  his  assistant,  Prof.  Duff  A. 
Abrams,  the  more  ideal  deformed  bar  is  described  as  follows  : 
(page  212,  Sec.  21)  :  "In  a  deformed  bar  of  good  design,  the 
projections  should  present  bearing  faces  as  nearly  as  possible 
at  right  angles  to  the  axis  of  the  bar. 

"The  areas  of  the  projections  should  be  such  as  to  preserve 
the  proper  ratio  between  the  bearing  stress  against  the  concrete 
ahead  of  projections  and  the  shearing  stress  over  the  surround- 
ing envelope  of  concrete." 

Regarding  the  twisted  bar,  Bulletin  71  says :  "The  tests  here 
recorded  show  conclusively  that  the  bond  resistance  of  twisted 
square  bars  is  inferior  in  characteristics  to  that  of  plain  round 
bars  of  similar  surface,  and  that  these  bars  have  little  or  no 
advantage  in  bond  resistance  within  limits  of  slip  which  would 
be  useful  in  structures. 

"  It  seems  strange  that  the  twisted  bar  has  gained  such  a  wide 
popularity  as   a   reinforcing   material." 

Further  (page  76),  "It  has  been  frequently  stated  that  cold 
twisting  is  effective  in  raising  the  yield  point  of  the  bar  by  over- 
stressing  a  portion  of  the  metal,  and  at  the  same  time  it  furnishes 
a  very  severe  test  on  the  quality  of  the  steel  itself. 

"However,  it  has  been  shown  by  tests  that  the  elastic  limit 
has  been  raised  on  only  a  portion  of  the  section  (the  outside) 
and  that  for  stresses  above  the  original  yield  point  the  modulus 
of  elasticity  of  the  whole  section  is  considerably  smaller  than 
the  normal  value  for  steel  within  the  elastic  limit.  In  other 
words,  for  stresses  above  the  original  yield  point  the  metal  in 
the  interior  of  the  section  will  be  stressed  beyond  its  elastic 
limit  and  the  rate  of  change  in  tensile  deformation  in  the  bar 
as  a  whole  will  be  larger  than  at  the  lower  stresses." 

The  corrugated  bars,  pages  36  and  37,  and  the  rib  bars  and 
corrugated  bar  described  on  next  page  come  nearer  to  the 
specifications  suggested  in  Bulletin  71  than  any  other  bars  in  the 
market. 


40 


REINFORCED    CONCRETE. 


Rib  Bars. — The  rib  bar  shown  by  Fig.  11  is  made  by  the 
Trussed  Concrete  Steel  Co.,  Detroit,  Mich.     The  projections 


Fig.    11.— Rib   Bar. 

on   the  bar  are   for  the   purpose   of  furnishing  a  mechanical 
bond.     Table  XIX  gives  sizes  and  weights. 


TABLE  XIX.— SIZES  AND  WEIGHTS  OF  RIB  BARS. 


Size,  ins 

Weight,  Ibs. 
per  ft. 

Size,  ins. 

Weight,  Ibs. 
per  ft. 

j 

0.48 
0.86 
1.35 
1.95 

i 

2.65 
3.46 
4.38 
4.51 

The  American  Deformed  Bar  comes  round  or  square  and 
is  rolled  by  several  mills  at  Chicago  and  St.  Louis. 

These  bars  have  same  areas  and  weights  as  plain  rounds 
or  squares  and  are  preferable  to  twisted  rods  or  to  bars  with 
closely  spaced  deformations  or  corrugations — and  appear  to 
have  a  maximum  bond  value  with  a  minimum  of  corru- 
gations. 

TESTS  MADE  BY  R.  W.  HUNT  &  Co.,  ON  HIGH  CARBON  DEFORMED  ROUND 
BARS.  AUGUST  22,  1911. 

Rods  used  for  the  Dallas-Oakcliffe  Reinforced  Concrete  "Viaduct: 

DU.  TENSILE  ELAST.  LIMIT  ELONG. 

1/8  in.  107,370  64,140  12.1% 

64,090  15    % 

62,000  13.7% 


8  in. 
Y*  in. 


104,000 
120,660 
100,520 


68.940 


15.6% 


MATERIALS  AND  MACHINES. 


41 


Table  XX  shows  results  of  experiments  made  by  Prof. 
A.  N.  Talbot  at  Urbana,  111.,  showing  the  remarkable  bond- 
ing strength  of  the  Collings  Bar,  which  is  similar  to  the 
American  Deformed  Bar,  but  wifh  deformations  like  those  on 
the  Rib  Bars,  page  40. 


Fig.    12. — American  Deformed  Bar. 


TABLE  XX. — DATA  OF  TESTS  OP  BOND  BETWEEN  CONCRETE  AND  STEEL. 
1,  1M,  2H  Concrete;  62  days  old.    All  specimens  from  same  batch. 


Length 

Maximum 

Stress  in 

Speci- 
men 

No. 

Kind  and  Size 
of  Bar. 

of 
Embed- 
ment, 

Bond 
Area, 
So, 

Maximum 
Load, 
Lbs. 

Bond 

Stress, 
Lbs.  per 

Steel  at 
Maximum 
Load, 

Method 
of  Failure. 

Ins. 

Ins. 

Sq.  In. 

Lbs.  per 
Sq.  In. 

1 

H'Rd.  Collings  Bar 

8.3 

13.05 

13,350 

1,020 

68,000 

Block  Split 

2 

H'Rd.  Collings  Bar 

8.2 

12.87 

20,200 

1,570 

104,200 

Block  Split 

3 

H"Rd.  Collings  Bar 

8.1 

12.70 

17,900 

1,410 

91,500 

Block  Split 

4 

y2"Rd.  Collings  Bar 

8.2 

12.87 

16,800 

1,300 

85,800 

Block  Split 

5 
6 

H*Rd.  Collings  Bar 
^"Rd.  Collings  Bar 

8.0 
8.3 

12.54 
19.50 

18,100 
17,100 

1,440 

878 

92,300 
38,700 

Block  Split 
Block  Split 

7 

^"Rd.  Collings  Bar 

8.1 

19.05 

19,700 

1,030 

44,700 

Block  Split 

8 

^"Rd.  Collings  Bar 

8.1 

19.05 

19,700 

1,030 

44,700 

Block  Split 

9 

3/T'Rd.  Collings  Bar 

8.1 

19.05 

18,600 

978 

42,200 

Block  Split 

10 

%*Rd.  Collings  Bar 

8.2 

19.30 

16,100 

836 

36,400 

Block  Split 

11 

1"  Rd.  Collings  Bar 

8.2 

25.7 

18,800 

732 

23,900 

Block  Split 

12 

l"Rd.  Collings  Bar 

8.0 

25.1 

17,700 

706 

22,500 

Block  Split 

13 

1*  Rd.  Collings  Bar 

8.1 

25.4 

17,500 

690 

22,300 

Block  Split 

14 

TRd.  Collings  Bar 

8.1 

25.4 

17,700 

696 

22,500 

Block  Split 

15 

l"Rd  Collings  Bar 

8.2 

25.7 

16,950 

660 

21,600 

Block  Split 

16 

M'  Plain  Round 

8.1 

19.05 

12,200 

640 

27,600 

Rod  pulled  out 

17 

%"  Plain  Round 

8.2 

19.30 

11,900 

617 

26,900 

Rod  pulled  out 

18 

%'  Plain  Round 

8.2 

19.3 

13,100 

678 

29,600 

Rod  pulled  out 

19 

%  "  Plain  Round 

8.1 

19.05 

13,500 

708 

-30,600 

Rod  pulled  out 

20 

%  *  Plain  Round 

8.0 

18.80 

13,700 

730 

31,000 

Rod  pulled  out 

Tests  made  May  5,  1910,  at  Urbana,  111. 


(Signed).  A.  N.  TALBOT. 


42 


REINFORCED    CONCRETE. 


Wire  Fabric. — This  material  has  come  into  almost  uni- 
versal use  and  has  been  found  to  possess  many  valuable, 
even  indispensable  qualities.  Its  advantages  are  that  it  pre- 
vents temperature  cracks  and  also  prevents  cracks  from 
shocks.  A  building  having  fabric  in  walls,  floors,  girders, 
beams,  columns,  and  resting  on  a  mat  foundation  can  with- 
stand unequal  loading,  treacherous  subsoil,  excessive  wind 
pressure,  fire  and  even  seismic  disturbances  much  better  than 
any  other  structure  known  to  the  technical  world. 

Wire  fabric  is  made  of  steel  wires  crossing  at  right  or 
oblique  angles  and  secured  at  the  intersections.  The  heavier 
wires  run  lengthwise  and  are  called  carrying  wires;  the 
lighter  ones  cross  these  and  are  called  distributing  or  tie 
wires.  The  manner  of  securing  the  intersections  has  given 

TABLE  XXI. 

AREA  IN  SQ.'!NS.  PER  ONE  FT.  IN  WIDTH. 


02 

American  Steel  &  Wire  Co.  Wire  Gage. 

Gage 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

Dia. 

.283' 

.263" 

.244* 

.225* 

.207' 

.192' 

.177* 

162* 

.148* 

.135* 
0143 

.121* 
.0114 

.106* 

.092* 

.080" 

.072' 

Area 

.0629 

.0541 

.0466 

.0399 

.0337 

.0290 

.0246 

0206 

.0173 

.0087 

.0066 

.0050 

.0041 

i* 
1H* 

.7538 

.6492 

.5592 

.4797 

.3944 

.3480 

.2952 

.2472 

.2076J.1722 

.1368 

.1044 
.0696 

.0792 
.0548 
.0396 

.0600 
.0400 
.0300 

.0492 
.0328 
.0246 

.5032 

.4328 

.3728 

.3192 

.2696 

.2320 

.1968 

.1648 

.1384 

.1144 

.0912 

2" 

.3774 

.3246 

.2796 

.2394 

.2022 

.1740 

.1476 

.1236 

.1038 

.0858 

.0684 

.0522 

VA" 

.3015 

.2597 

.2237 

.1917 

.1577 

.1392 

.1181 

.0989 

.0828 

.0689 

.0544 

.0417 

.0397 

.0160 

.0197 

3* 

.2516 

.2164 

.1864 

.1596 

.1348 

.1160^.0984 

0824 

.0692 

.0572 

.0456 

.0348 

.0264 

.0200 

.0164 

4* 

.1887 

.1623 

.1398 

.1197 

.1011 

.0870 

.058p 
.0497 

.0738 

.0618 

.0519 

.0429 

.0342 

.0261 

.0198 

.0150 

.0123 

5* 

.1507 

.1258 

.1118 

.0959 

.0759 

.0590 

0494 

.0415 

.0344 

.0273 

.0209 

.0158 

.0120 

.0098 

6* 

.1258 

.1082 

.0932 

.0798 

.0674 

.0492 

0412 

.0346 

.0286 

.0228 

.0174 

.0132 

.0100 

.0082 

7' 

.1077 

.0924 

.0799 

.0685 

.0535 

.0422 

0353 

.0287 

.0246 

.0196 

.0149 

.0113 

.0086 

.0073 

8' 

.0943 

.0821 

.0689 

.0598 

.0505 

.0435 

.0369 

0309 

.0259'.0214 

.0171 

.0130 

.0099 

.0075 
.0066 
.0050 

.0061 
.0055 

9" 

.0837 

.0721 

.0691 

.0533 

.0439 

.0387 

.0328 

0275 

.023l|.0169 

.0152 

.0115 

.0088 

12' 

.0629 

.0541 

0466 

.0399 

0337 

.0290 

.0246 

0206 

.0173 

.0143 

.0114 

.0087 

.0066 

.0041 

MATERIALS  AND  MACHINES. 


43 


rise  to  a  number  of  different  types  of  wire  fabric,  several  of 
the  principal  ones  of  which  are  given  below.  The  manu- 
facturers of  each  of  these  forms  will  furnish  fabric  in  special 
size  of  wire  and  mesh  if  desired. 

Triangle  Mesh  Steel  Woven  Wire  Reinforcement  is  made 
with  both  single  and  stranded  longitudinal,  or  tension  mem- 
bers. That  with  the  single  wire  longitudinal  is  made  with 
one  wire  varying  in  size  from  a  No.  12  gage  up  to  and 
including  a  ^-inch  diameter,  and  that  with  the  stranded 
longitudinal  is  composed  of  two  or  three  wires  varying  from 
No.  12  gage  up  to  and  including  No.  4  wires  stranded  or 
twisted  together  with  a  long  lay.  These  longitudinals  either 
solid  or  stranded  are  invariably  spaced  4-inch  centers,  the 
sizes  being  varied  in  order  to  obtain  the  desired  cross  sec- 
tional area  of  steel  per  foot  of  width. 

The  transverse  or  diagonal  cross  wires  are  so  woven  be- 


\/\ 


i3. — 4-Inch  Triangle  Mesh  Reinforcement. 


44  REINFORCED    CONCRETE. 

TABLE  XXII. 

LONGITUDINALS  SPACED  4-iNcn  CENTERS. 
CROSS  WIRES  SPACED  2-iNCH  CENTERS. 

Number  and  Gage  of  Wires,  Areas  per  Foot  Width  and  Weights  per  100  Square  Feet. 
Styles  Marked  *  Usually  Carried  in  Stock. 


Style 
Number 

No.  of 
Wires 
Each 
Long. 

Gage 
of  Wire 
Each 
Long. 

Gage 
of  Cross 
Wires 

Sectional 
Area 
Long 
Sq.  In. 

Sectional 
Area 
Cross 
Wires 
Sq.  In. 

Cross 
Sectional 
Area 
per  Ft. 
Width 

Approxi- 
mate 
Weight 
per  100 
Sq.  Ft. 

4-A 

6 

14 

.087 

.050 

.102 

53 

5-A 

8 

14 

.062 

.050 

.077 

44 

6-A 

10 

14 

.043 

.050 

.058 

37 

*  7-A 

12 

14 

.026 

.050 

.041 

31 

23-A 

/4" 

12H 

.147 

.076 

.170 

86 

24-A 

4 

12H 

.119 

.076 

.142 

76 

25-A 

( 

5 

12^ 

.101 

.076 

.124 

70 

26-A 

12H 

.087 

.076 

.110 

64 

27-A 

8 

mi 

.062 

.076 

.085 

55 

*28-A 

10 

WA 

.043 

.076 

.066 

48 

29-A 

12 

U1A 

.026 

.076 

.049 

42 

31-A 

2 

4 

WA 

.238 

.076 

.261 

120 

32-A 

2 

5 

i2H 

.202 

.076 

.225 

107 

33-A 

2 

6 

12H 

.174 

076 

.196 

97 

34-A 

2 

8 

WA 

.124 

.076 

.146 

78 

35-A 

2 

10 

121A 

.086 

.076 

.109 

64 

36-A 

2 

12 

l^A 

.052 

.076 

.075 

52 

38-A 

3 

4 

12^ 

.358 

.076 

.380 

165 

39-A 

3 

5 

12H 

.303 

.076 

.325 

145 

40-A 

3 

6 

12H 

.260 

.076 

.283 

129 

41-A 

3 

8 

12H 

.185 

.076 

.208 

101 

42-A 

3 

10 

12^ 

.129 

.076 

.151 

81 

43-A 

3 

12 

12H 

.078 

.076 

.101 

C2 

Special  Sizes  on  Application. 
Length  of  Rolls:    150-ft.,  300-ft.  and  600-ft. 
Widths:    18-in.,  22-in.,  26-in.,  30-in.,  34-iu.,  38-in.,  42-in.,  46-in.,  50-in.,  54-in.  and  58-in. 


MATERIALS  AND  MACHINES. 


45 


TABLE  XXII-A. — AREAS  IN  SQUARE  FEET  PER  ROLL  OF 
TRIANGLE  MESH  REINFORCEMENT 


Width  of  Roll 
in  Inches 

Square  Feet  of  Reinforcement  in  Roll 

150-ft.  Roll 

300-ft.  Roll 

600-ft.  Roll 

18 

225 

450 

900 

22.  .........  

275 

550 

1100 

2G.'.'..  '.'.'.'.'.'.'.'........'..'..........'. 

325 

650 

1300 

375 

750 

1500 

34... 

425 

850 

1700 

00 

475 

950 

1900 

12...'..'.'..'.'.'.'.'.'.'.'.'.'.'.'....'.'.'....... 

525 

1050 

2100 

575 

1150 

2300 

50... 

625 

1250 

2500 

54 

675 

1350 

2700 

58  

725 

1450 

2900 

As  indicated  in  the  above  table,  Triangle  Mesh  Reinforcement  is  made  up  in  the  following 
widths:  18,  22,  26,  30,  34,  38,  42,  46,  50,  54  and  58  inches,  and  in  standards  lengths  of  rolls 
of  150,  300  and  600  feet. 

For  the  lighter  styles,  rolls  of  any  of  the  above  lengths  may  be  used.  Material  of  medium 
weights  is  recommended  to  be  used  in  150  or  300  foot  lengths,  while  with  the  heaviest  styles 
it  is  more  conveniently  handled  in  rolls  containing  150-foot  lengths. 

TABLE  XXII-B. 

LONGITUDINALS  SPACED  4-iNCH  CENTERS. 
CROSS  WIRES  SPACED  4-iNcn  CENTERS. 

Number  and  Gage  of  Wires,  Areas  per  Foot  Width  and  Weights  per  100  Square  Feet. 
Styles  Marked  *  Usually  Carried  in  Stock. 


Style 
Number 

No.  of 
Wires 
Each 
Long. 

Gage 
of  Wire 
Each 
Long. 

Gage 
of  Cross 
Wires 

Sectional 
Area 
Long 
Sq.  In. 

Sectional 
Area 
Cross 
Wires 

Cross 
Sectional 
Area 
per  Ft. 
Width 

Approxi- 
mate 
Weight 
per  100 
Sq.  Ft. 

*  4 

6 

14 

.087 

.025 

.102 

43 

5 

8 

14 

.062 

.025 

.077 

34 

6 

10 

14 

.043 

.025 

.058 

27 

*  7 

12 

14 

.026 

.025 

.041 

21 

*23 

M* 

12H 

.147' 

.038 

.170 

72 

24 

4 

12^2 

.119 

.038 

.142 

62 

25 

5 

12H 

.101 

.038 

.124 

55 

*26 

1 

6 

12J4 

.087 

.038 

.110 

50 

*27 

1 

8 

12^ 

.062 

.038 

.085 

41 

28 

1 

10 

12/^ 

.043 

.038 

.066 

34 

29 

1 

12 

12^2 

.026 

.038 

.049 

28 

31 

2 

4 

12}/jj 

.238 

.038 

.261 

106 

32 

2 

5 

12H 

.202 

.038 

.225 

92 

33 

2 

6 

12}^ 

.174 

.038 

.196 

82 

34 

2 

8 

12V6 

.124 

.038 

.146 

63 

35 

2 

10 

12|i 

.086 

.038 

.109 

50 

36 

2 

12 

.052 

.038 

.075 

37 

*38 

3 

4 

121A 

.358 

.038 

.380 

151 

39 

3 

5 

l2}/2 

.303 

.038 

.325 

130 

40 

3 

6 

121A 

.260 

.038 

.283 

114 

41 

3 

8 

12/^ 

.185 

.038 

.208 

87 

*42 

3 

10 

12H 

.129 

.038 

.151 

66 

43 

3    ; 

12 

i|y 

.078 

.038 

.101 

47 

Special  Sizes  on  Application. 
Length  of  Rolls:    150-ft.,  300-ft.  and  600-ft. 
Widths:   18-in.,  22-in.,  26-in.,  30-in.,  34-in.,  38-in.,  42-in.,  46-in.,  50-in.,  54-in.  and  58-in. 


46  REINFORCED    CONCRETE. 

tween  the  longitudinals  that  perfect  triangles  are  formed  by 
their  arrangement,  thereby  not  only  lending  additional  carry- 
ing strength  to  the  longitudinal  or  tension  members,  but 
positively  spacing  them  and  providing  a  most  perfect  dis- 
tribution of  the  steel.  These  diagonal  cross  or  transverse 
wires  are  woven  either  2  or  4  inches  apart,  as  is  desired.  It 
is  the  most  perfect  reinforcement  for  concentrated  loads, 
distributing  the  stress  imposed  by  the  load  throughout  the 
floor  slab.  A  hinge  joint  is  provided  on  each  longitudinal, 
which  enables  this  reinforcement  to  be  folded  longitudinally 
in  any  desired  shape,  making  it  adaptable  to  all  kinds  of  con- 
crete construction.  Its  design  provides  a  most  perfect  me- 
chanical bond  between  the  steel  and  the  concrete,  and  from 
the  fact  that  it  is  not  galvanized  (unless  specially  ordered) 
the  maximum  adhesive  bond  is  developed. 

A  sufficient  area  of  steel  is  provided  in  the  cross  wires  of 
Triangle  Mesh  Reinforcement  to  prevent  temperature  cracks, 
thereby  eliminating  the  necessity  of  laying  additional  re- 
inforcement at  right  angles  to  the  longitudinal  or  tension 
members. 

Lock-Woven  Fabric. — Lock-woven  fabric,  Fig.  15,  is  man- 
ufactured by  W.  N.  Wight  &  Co.,  New  York.  The  wires  are 
from  No.  3  to  No.  12  gage,  commonly  woven  in  4x6-in.  mesh, 
56  ins.  wide  and  300  ft.  long. 


-$==t 


Fig     15  — Lock-woven    Fabric.  Fig.     16. — American     Wire 

Fabric. 

American  Wire  Fabric. — American  wire  fabric,  Fig.  16,  is 
of  high  carbon  steel  wires,  secured  at  the  intersections  by 
No.  14  wire,  and  manufactured  by  the  American  Wire  Fence 
Co.,  Chicago.  Standard  sizes  are  shown  by  Table  XXIII. 


MATERIALS  AND  MACHINES. 


47 


TABLE  XXIII. — GAGE  AND    MESH   OF   AMERICAN  WIRE 
FABRIC. 


Gage  of 

Carrying 
Wires. 

Gage  of 
Distributing 
Wires. 

Mesh 
in 
Inches. 

9 
9 
9 

7 
7 

11 
11 
11 

11 
11 
11 

4x  12 
4x6 
6x6 

4x12 
4x6 
6x6 

Welded  Wire  Fabric.— Welded  wire  fabric,  Fig.  17,  has 
the  intersections  electrically  welded  and  is  manufactured  by 
the  Clinton  Wire  Cloth  Co.,  Clinton,  Mass.,  in  a  variety  of 
meshes — the  longitudinals  spaced  in  steps  of  l/z  in.  and  the 
transverse  wires  in  steps  of  1  in. 


TABLE  XXIV. — WEIGHT    AND    STRENGTH    OP    WELDED 
WIRE  FABRIC. 


Fig.    17.— Welded 
Wire  Fabric. 


Gage 
W.  &M. 

Diameter 
of 
One  Wire 

Wt.  per  Lineal 
Foot  of 
One  Wire 

Tensile 
Strength  of 
One  Wire 

No. 

in  ins. 

in  Ibs. 

in  Ibs. 

0 

.3065 

.2506 

4,427 

1 

.2830 

.2136 

3,774 

2 

.2625 

.1838 

3,247 

3 

.2437 

.1584 

2,799 

4 

.2253 

.1354 

2,392 

5 

.2070 

.1143 

2,019 

6 

.1920 

.0983 

1,737 

7 

.1770 

.0835 

1,476 

8 

.1620 

.0700 

1,237 

9 

.1483 

.0586 

1,036 

10 

.1350 

.0486 

859 

11 

.1205 

.0387 

684 

12 

.1055 

.0296 

524 

The  following  figures*   show  a  comparison  between  two 
kinds  of  wire  as  to  breaking  loads: 


*By  Lorin  E.  Hunt,  C.  E.,  Berkeley,  Cal. 


48 


REINFORCED    CONCRETE. 


Diameter 
in  inches. 

Breaking  loaa 
in  Ibs. 

Load 
per  sq.  in. 

Welded  Fabric  No   8 

0  163 

1  510 

72  300 

Welded  Fabric  No.  6.  

0  191 

1  860 

64  900 

0  146 

2  292 

136  900 

American  System  No.  7  

0.175 

3,060 

127,100 

I "7 J 

Fig.   18.— Expanded  Metal. 

Expanded  Metal. — Expanded  metal,  Fig.  18,  is  a  mesh 
formed  from  a  sheet  of  soft  steel  by  slitting  and  opening  or 
expanding  the  metal  with  meshes  in  direction  normal  to  the 
axis  of  the  sheet.  Table  XXV  is  compiled  from  information 
furnished  by  the  Associated  Expanded  Metal  Companies, 
New  York. 


Fig.   19.—  Kahn  Rib  Metal. 

Kahn  Rib  Metal. — This  material,  Fig.  19,  is  made  from  a 
sheet  of  metal,  flat  on  one  side  and  corrugated  on  the  other. 
Strips  of  the  metal  adjacent  to  the  ribs  are  stamped  out,  and 
the  sheet  is  drawn  out  into  square  meshes.  The  illustration 
shows  these  points  and  Table  XXVI  gives  the  properties  of 


MATERIALS  AND  MACHINES. 


49 


this  material.     It  is  manufactured  by  the  Trussed  Concrete 
Steel  Co.,  Detroit,  Mich. 

TABLE  XXV. — EXPANDED  METAL  MESHES. 


Designation 

Size  of  Mesh 

d 

^ 

Secti'n 

Size  of 

•S 

rQ     M 

I 

1 

in 

standard 

w 

.si 

«5 

1 

Thick- 

Width 
center 

Leng'h 
center 

Strand 

sq.  in. 
per 

Wt. 
in  Ibs 

sheets, 
in  feet 

II 

e 

t/5 

ness 

to 

to 

foot 

per 

w  3 

o-oo 

'~ 

in 

center 

center 

of 

sq.  ft. 

Width  by 

to'D 

Wn_, 

,4  t    Q 

1 

bo 
ctf 

ins. 

in 

in 

width 

length 

O 

o 

I 

ins. 

ins. 

£; 

d'Q 

w 

j 

S5 

18 

0.049 

0.43 

1.2 

Standard 

.209 

.74 

3  or  6x8 

5 

120 

13 

0.095 

0.95 

2.0 

" 

.225 

.80 

6x8  or  12 

5 

240 

12 

0.109 

1.36 

3.0 

" 

.207 

.70 

4x8  or  12 

5 

160 

2 

12 

0.109 

1.82 

4.0 

" 

.166 

.56 

5x8  or  12 

5 

200 

3 

16 

0.065 

3.00 

8.0 

" 

.083 

.28 

6x8  or  12 

10 

480 

3 

10 

0.134 

3.0 

8.0 

Light 

.148 

.50 

Six  8  or  12 

5 

210 

3 

10 

0.134 

3.0 

8.0 

Standard 

.178 

.60 

6x  8  or  12 

.5 

240 

3 

10 

0.134 

3.0 

8.0 

Heavy 

.267 

.90 

4x8  or  12 

5 

160 

3 

10 

0.134 

3.0 

8.0 

Ex.  Heavy 

.356 

1.20 

6x8  or  12 

3 

144 

3 

6 

0.203 

3.0 

8.0 

Standard 

.400 

1.38 

5x8  or  12       3 

120 

3 

6 

0.203 

3.0 

8.0 

Heavy 

.600 

2.07 

5x8  or  12      3 

120 

4 

16 

0.065 

3.86 

6.85 

Old  Style 

.093 

.42 

4|x8or  9 

6 

206 

6 

4 

0.238 

6.0 

16.0 

Standard 

.245 

.84 

5x8  or  12      5 

200 

6 

4 

0.238 

6.0 

16.0 

Heavy 

.368 

1.26 

5x8  or  12 

3 

120 

LATHING. 


Size  of 

Mesh 

Designation 

Width 
center 
to 
center 
in 
inches 
w 

Leng'h 
center 
to 
center 
in 
inches 
/ 

Gage 
U.S. 
Stand- 
ard 

Thick- 
ness 
inches 

Size  of 
sheets 
in  feet 

Sheets 
in  a 
bundle 

Sq. 
yds. 
in  a 
bundle 

Wt. 
in  Ibs. 
per 
sq.  yd. 

A 
B 
BB 

Diamond, 
Ho.  24 
Diamond, 
No.  26 

*0.40 
*0  .  40 
-0.60 
0.41 

0.41 

*2.0 
*2.0 
62.0 
1.2 

1.2 

24 
27 
27 

24 

26 

.025 
.0171875 
.0171875 

.025 
.01875 

18x96 
18x96 
22x96 

18x96 
24x96 

9 
15 
15 

15 
9 

12. 
20. 

24.44 

20. 
16. 

4.00 
2.90 
2.33 

3.75 
2.66 

*The  meshes  of  "A"  and  "B"  lath  are  parallelograms,  the 
sides  being  0.6x1.5  ins.  on  centers,  and  the  perpendicular  distance 
between  centers  of  long  sides  is  about  0.4  in.  "BB"  lath  is  practi- 
cally the  same  as  "B"  except  meshes  are  wider.  The  tensile 
strength  of  the  uncut  sheet  is  16,000  Ibs.  per  sq.  in. 


50 


REINFORCED   CONCRETE. 


TABLE  XXVI. — PROPERTIES  OF  KAHN  RIB  METAL. 


Distance 

Sect,  area 

Size 
No. 

center 
to 
center 

in  sq.  ins. 
per  ft. 
in 

Width 
of  sheets 
ins. 

Sq.  ft. 
in  sheet 
12ft. 

Safe 
tensile 
stress, 

Ultimate 
strength 

Weight, 
Ibs.  per 
sq.  ft. 

of  bars, 

width 

long 

Ibs. 

in  ins. 

2 

2 

0.54 

17 

17 

9,700 

38,800 

2.13 

3 

3 

0.36 

25 

25 

6,480 

25,920 

1.43 

4 

4 

0.27 

33 

33 

4,860 

19,440 

1.08 

5 

5 

0.22 

41 

41 

3,960 

15,840 

0.87 

6 

6 

0.18 

49 

49 

3,240 

12,960 

0.72 

7 

7 

0.15 

57 

57 

2,700 

10,800 

0.62 

8 

8 

0.14 

65 

65 

2,520 

10,080 

0.55 

NOTE. — Area  of  each  rib  is  0.08  sq.  in.     Standard  lengths  of  sheets  are  12, 
14  and  16  ft. 

Beam  and  Girder  Units. — There  are  several  forms  of 
beam  or  girder  reinforcement  which  are  either  in  one  piece 
or  assembled  together  as  one  unit,  the  steel  being  placed 
along  the  planes  of  greatest  stress.  A  number  of  the  best 
known  forms  are  given  below.  In  nearly  all  of  these  built- 
up  forms,  deformed  bars  can  be  used  instead  of  plain  rods, 
according  to  the  choice  of  the  engineer. 


Fig.    20.— Cummings   Girder  Frame. 

Cummings  Girder  Frame. — The  Cummings  trussed  girder 
reinforcement  is  arranged  as  a  framed  system  by  the  intro- 
duction of  hoop  iron  chair-clamps  around  all  rods  where  one 
of  them  is  bent  up.  The  rods  are  shipped  flat  to  the  build- 
ing for  the  sake  of  convenience,  as  shown  at  C,  D  and  E, 
Fig.  20.  The  prongs  are  bent  up  at  45  degrees  (as  at  A)  on 
the  floor  before  the  frame  is  set  in  the  mold,  the  chairs 


MATERIALS  AND   MACHINES. 


51 


further  serving  to  keep  the  bars  at  proper  distance  from  the 
molds. 

Pittsburgh  Steel  Products  Co.'s  Beam  Reinforcement  con- 
sists of  electrically  welded  frames  with  shear  bars  inclined 
45°  with  the  horizontal  and  spaced  at  the  theoretically  cor- 
rect points. 

The  bottom  horizontals  consist  of  two  members  placed 
one  above  the  other  with  a  clearance  of  ^  inch,  the  upper 
of  the  two  being  cut  off  at  the  correct  theoretical  point  so 
as  to  prevent  a  waste  of  material,  which  results  when  the 
same  cross  section  of  metal  extends  for  the  full  length  of  the 
beam  or  girder. 

The  top  bars  at  supports  extend  a  sufficient  distance  be- 
yond the  support  to  develop  the  full  strength  of  the  bars  so 
as  to  protect  the  stresses  of  negative  moments,  causing 
cracks  over  supports. 

The  shear  bars  are  spaced  from  4  inches  on  centers  to 
not  exceeding  the  depth  of  the  beam. 

The  Xpantrus  Bar  is  of  similar  appearance  to  the  Pitts- 
burgh Steel  Products  Co.'s  bar,  but  is  manufactured  by  slit- 
ting and  expanding  both  ends. 

Continuity  over  supports  is  produced  by  pin  connection 
as  of  course  the  top  bar  cannot  extend  beyond  the  bottom 
bar,  being  sheared  from  the  same  metal. 

"Unit"  Frame.— The  Unit  concrete-steel  frame,  Fig.  21, 
has  the  reinforcing  rods  and  stirrups  rigidly  held  together 
by  a  unit  socket  support,  which  latter  also  serves  the  pur- 
pose of  receiving  hanger  bolts  or  other  appliances  that  are 


Fig.    21.— Unit    Frame. 

to  be  suspended  to  the  girder  afterwards. 

Kami  Trussed  Bar.— The  Kahn  trussed  bar,  Fig.  22,  named 
for   its   inventor,   is   a   form   of   beam,   girder   or   column    re- 


52 


REINFORCED   CONCRETE. 


inforcement,  consisting  of  a  special  rolled  section  of  steel 
with' diagonal  members  sheared  up  at  45°  on  both  sides  of 
the  main  body.  For  continuous  beams,  inverted  bars  are 
placed  over  the  supports  in  the  upper  part  of  the  beam,  ex- 
tending over  the  region  of  tension.  These  bars  are  of  two 
forms  of  section,  as  shown  by  Fig.  22,  and  either  form  may 
be  sheared  alternately  or  opposite  with  varying  lengths  of 
diagonal.  They  are  manufactured  by  the  Trussed  Concrete 
Steel  Co.,  Detroit,  Mich. 


Fig.    22.— Kahn    Trussed    Bar. 
TABLE  XXVII. — PROPERTIES  OP  KAHN  TRUSSED  BARS. 


Size 

Weight 

Area  of 
un- 

Area  of 

Shear 
value 

Tensile   strength 
of  bar 

Length  of 
Diagonals 

in 

in 

sheared 

sheared 

of  one 

in  Ibs.   per  sq.  in. 

in  ins. 

ins. 

Ibs. 

bar  in 

bar  in 

diagon'l 

per  ft. 

sq.  ins 

sq.  ins. 

in  Ibs. 

a  x  b 

per 

Un- 

Stand- 

Gross. 

Net. 

sq.  in. 

sheared. 

Sheared  . 

ard. 

Special. 

Square  Section  Bars. 


JxU 

1.4 

.41 

.25 

900 

6,600 

4,000 

6 

Ix2f 

2.7 

.79 

.56 

1,300 

12,600 

9,000 

12 

8 

1    x3 

4.8 

1.41 

1.00 

2,300 

22,600 

16,000 

24 

18 

Hx3f 

6.8 

2.00 

1.60 

2,300 

32,000 

25,600 

24 

/      18 
I      30 

C   X   d 

New  Section  Bars. 

Ifx2f 

6.8 

2.00 

1.60 

2,300 

32,000 

25,600 

24 

/      30 

2    x  3i 

10.2 

3.00 

2.40 

3,400 

48,000 

38.400 

24 

I      18 
30 

NOTE. — 6,  8  and  12  in.  diagonals  are  sheared  opposite.      18,  24  and  30  in. 
diagonals  are  sheared  alternately. 


MATERIALS  AND  MACHINES.  S3 

Luten  Truss. — The  Luten  truss  is  clamped  and  locked  in 
a  rigid  unit  by  means  of  a  clamp  with  a  wedge  that  is  self- 
locking  when  tightly  driven  in.  The  truss  and  one  of  the 
clamps  in  position  are  shown  by  Fig.  23.  This  truss  is  to  be 
obtained  from  the  National  Concrete  Co.,  Indianapolis,  Ind. 


Fig.   23. — Luten  Truss. 

Hooped  Column  Reinforcement.— While  there  are  several 
types  of  reinforced  concrete  column  constructed,  almost  the 
only  assembled  units  on  the  market  are  those  for  hooped  col- 
umns, since  the  other  types  of  column  reinforcement  are 
assembled  in  the  field  from  loose  rods.  As  with  wire  fab- 
rics and  girder  units,  the  main  points  of  difference  in  hooped 
column  reinforcements  are  the  methods  of  fastening.  The 
hoops  may  be  arranged  either  as  a  spiral  or  as  annular  rings, 
and  the  hooping  material  may  be  either  flat  band  steel  or 
wires.  The  longitudinal  reinforcement  may  be  part  of  the 
hooping  unit  or  separate  rods  may  be  inserted.  The  supe- 
rior advantages  of  hooped  columns  over  other  forms  are  re- 
ferred to  under  Design. 

Cummings  Hooped  Column. — The  Cummings  hooped  col- 
umn, invented  by  Mr.  Robert  A.  Cummings,  is  shown  by 
Fig.  26.  Table  XXVIII  gives  the  safe  loads.  This -column 
reinforcement  is  built  up  of  annular  hoops  made  of  flat  steel 
bent  to  a  circle  with  the  ends  riveted  or  welded  together  in 
such  a  manner  that  the  ends  of  the  hoops  protrude  at  right 
angles  to  keep  them  the  proper  distance  from  the  mold. 
The  vertical  reinforcement  is  often  made  of  angles  with 
holes  punched  at  intervals  for  staples  to  fasten  them  to  the 
hoops. 


54 


REINFORCED   CONCRETE. 


TABLE  XXVIII. — HOOPED  COLUMNS,  CUMMINGS  SYSTEM. 
(Factor  of  Safety  =  4.) 


Size  of 

Column, 
inches. 

Diameter 
of  Hoops, 
inches. 

Breadth 
and  Gage 
of  Hooping 
Steel. 

Distance 
c.c.of  hoops 
inches. 

No.  and 
Size  of 
Verticals. 

Wt.  of 
Steel 
per  lin.  ft. 

Safe  load 
for  Col., 
in  Ibs. 

12 

10 

-  18 

2 

_ 

7.5 

99,500 

14 

12 

-  16 

2 

_ 

9.27 

143,000 

16 

13 

*   -  16 

3 

_ 

11.88 

166,400 

18 

15 

t    -  14 

3 

_ 

14.44 

223,500 

20 

17 

i    -  14 

3 

_ 

17.52 

277,000 

22 

19 

i    -  14 

3 

_ 

I 

20.93 

336,200 

24 

21 

J    -  12 

3 

6- 

i 

26.84 

430,500 

26 
28 
30 
32 

23 
25 
27 
29 

1    -  12 
i    -12 
i    -  10 
i    -  10 

3 
3 
3 
3 

6  - 
6  - 
8  - 
8  - 

31.74 
32.88 
43.55 
45.05 

505,700 
575,000 
704.500 
786,500 

34 

31 

!    -  10 

3 

6  - 

i 

50.15 

884,200 

36 

33 

*    -  8 

3 

6  - 

1 

57.69 

1.036  ,200 

38 

35 

1    -  8 

3 

6  - 

H 

59.45 

1,136,200 

American  Hooped  Column. — The  American  system  of  col- 
umn reinforcement  is  illustrated  by  Fig.  27.  The  spiral  is 
made  of  high  carbon  steel.  Table  LVIII,  page  157,  compiled 
from  Considered  formula,  gives  the  ultimate  loads  for  this 
form  of  column  reinforcement.  The  manufacturers  are  the 
American  Wire  Fence  Co.,  Chicago. 

JnL 


Fig.    26.— Cummings  Figr.    27.— American    Hooped 

Hooped    Column.  Column. 

Smith  Hooped  Column. — Fig.  29  shows  an  assembled 
view  and  Fig.  30  a  detail  of  a  hooped  reinforcement  for  con- 
crete columns  made  by  the  F.  P.  Smith  Wire  &  Iron  Works, 
Chicago,  111.,  and  used  for  some  4,000  columns  in  the  large 


MATERIALS  AND  MACHINES. 


55 


new  warehouse  of  reinforced  concrete  built  for  Mont- 
gomery Ward  &  Co.,  at  Chicago,  111.  The  reinforcement,  as 
shown,  is  made  up  in  units  of  any  length  and  diameter  and 
of  any  shape  bar  and  size  of  hooping  specified.  Ordinarily 
the  bars  used  are  plain  flats  with  rounded  edges,  as  shown, 
and  four  bars  are  used.  The  bars  are  fixed  to  rotating  heads 
and  the  hooping  wire  wound  into  the  rounded  holes,  which 
are  then  closed  by  a  hammer  blow  on  the  projecting  fin  or 
point.  The  pitch  of  the  hooping  can  be  made  as  desired. 

These  spirals  are  shipped  knocked  down  or  in  collapsed 
form,  whereby  a  much  lower  freight 
rate  is  obtained. 


Fig.  29. — Smith  Hooped  Column. 


Fig.   30. — Connection  of  Hoops 
to  Verticals,  Smith  Column. 


Structural  Steel. — The  following  tables  include  those 
forms  of  structural  steel  which  may  be  used  for  reinforcing 
purposes.  Standard  Carnegie  I-beams  and  channels  are  giv- 
en by  Tables  XXIX  and  XXX.  These  are  often  used  in 
beams  and  columns,  which  are  afterward  encased  in  con- 
crete. Tables  XXXI  to  XXXIV  show  corresponding  data 
for  angles.  Table  XXXV  is  inserted  as  being  useful  in  de- 
termining the  areas  and  numbers  of  steel  rods  required  for  a 
given  percentage  of  reinforcement. 

The  properties  of  sections  are  given  in  Table  XXXVI. 


56 


REINFORCED   CONCRETE. 


TABLE  XXIX.— PROPERTIES  OF  STANDARD  CARNEGIE  I-BEAMS. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

~~ 

•W 

. 

g 

. 

«„     .52  d 

-3 

<2d 

1 

•s-s 

•5-S 

S-t 
*-•      • 

|| 

P 

la 

•+-*    (T> 

t>  .*3-g 
Iplll 

111  iff 

J'ihf-p! 

1 

la 

Qi 

fS 

"o  w 
|.S 

H 

-3% 

M 

PH 

ill  III 

•  SB** 

I 

!' 

r 

B5 

~15~ 

60.00 

17.67 

0.590 

6.000 

609.0 

25.96 

5  87 

B7 

15 

42.00 

12.48 

0.410 

5.500 

441.7 

14.62 

5.95 

B8 

12 

40.00 

11.84 

0.460 

5.250 

268.9 

13.81 

4.77 

B9 

12 

31.50 

9.26 

0.350 

5.000 

215.8 

9.50 

4  83 

Bll 

10 

25.00 

7.37 

0.310 

4.660 

122.1 

6.89 

4.07 

B13 

9 

21.00 

6.31 

0.290 

4.330 

84.9 

5.16 

3.67 

B15 

8 

18.00 

5.33 

0.270 

4.000 

56.9 

3.78 

3.27 

B17 

7 

15.00 

4.42 

0.250 

3.660 

36.2 

2.67 

2.36 

B19 

6 

12.25 

3.61 

0.230 

3.330 

21.8 

1.85 

2.46 

B21 

5 

9.75 

2.87 

0.210 

3.000 

12.1 

1.23 

2  05 

B23 

4 

7.50 

2.21 

0.190 

2.660 

6.0 

0.77 

1.64 

B77 

3 

5.50 

1.63 

0.170 

2.330 

2.5 

0.46 

1.23 

TABLE  XXX. — PROPERTIES  OF  STANDARD  CARNEGIE  CHANNELS. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

K 

O 

c 

d 

"o  tn 

•3    fl|- 

•as. 

•  a 

Section  Ind 

°S 
•Si! 

P.  C 

«l 

o 

f 

Area  of 
Section 
in  sq.  ins 

Thickness 
Web  in  in 

Width  oi 
Flange  in  i 

-J2  ^  rt    • 
40  rt<  o      vj 

mm 

o£?  »0o 

*  ir 

SI 

i 

J/ 

r 

01 

15 

33.00 

9.90 

0.400 

3.400 

312.6 

8.23 

5.62 

C2 

12 

20.50 

6.03 

0.280 

2.940 

128.1 

3.91 

4.61 

03 

10 

15.00 

4.46 

0.240 

2.600 

66.9 

2.30 

3.87 

04 

9 

13.25 

3.89 

0.230 

2.430 

47.3 

1.77 

3.49 

05 

8 

11.25 

3.35 

0.220 

2.260 

32.3 

1.33 

3.11 

C6 

7 

9.75 

2.85 

0.210 

2.090 

21.1 

0.98 

2.72 

07 

6 

8.00 

2.38 

0.200 

1.920 

13.0 

0.70 

2.34 

08 

5 

6.50 

1.95 

0.190 

1.750 

7.40 

0.48 

1.95 

C9 

4 

5.25 

1.55 

0.180 

1.580 

3.80 

0.32 

1.56 

072 

3 

4.00 

1.19 

0.170 

1.410 

1.60 

0.20 

1.17 

For  each  of  the  above  tables: 

L  =  Safe  load  in  pounds  uniformly  distributed;   7=span  in  feet. 
M  =  Moment  of  forces  in  foot  pounds ;  C  and  C'  =  coefficients  given  on  oppo- 
site page. 


MATERIALS  AND  MACHINES. 


57 


TABLE  XXIX.     (Continued). — PROPERTIES  OF  STANDARD  CARNEGIE  I-BEAMS 


10 

11 

12 

13 

14 

15 

C* 

•S  eJ'Sl 

J_, 

c  9*3  g  2  ^ 

„£* 

^•!y  . 

J$a*«! 

9 

0  §<£  r  . 

IHJ.1 

rt  >>  g  o  -^ 

«o||g 

*°u 

iiifi! 

co,|  3  P,OO 

**£s 

°  C  5t3'0  « 

lllPl 

Ifiill 

T3 
c 
i—  i 

r' 

S 

o^c 

^C' 

1.21 

81.2 

866100 

876600    . 

11.49 

B5 

1.08 

58.9 

628300 

490800 

11.70 

B7 

1  08 

44.8 

478100 

373500 

9.29 

B8 

1  01 

36.0 

383700 

299700 

9.45 

B9 

0.97 

24.4 

260500 

203500 

7.91 

Bll 

0.90 

18.9 

201300 

157300 

7.12 

B13 

0.84 

14.2 

151700 

118500 

6.32 

B15 

0.78 

10.4 

110400 

86300 

5.53 

B17 

0.72 

7.3 

77500 

60500 

4.70 

B19 

0.65 

4.8 

51600 

40300 

B21 

0  59 

3  0 

31800 

24900 

'     B23 

0.53 

1.7 

17600 

13800 

B77 

TABLE  XXX.    (Continued). — PROPERTIES  OF  STANDARD  CARNEGIE  CHANNELS. 


10 

11 

12 

13 

14 

15 

16 

Radius  of 
Gyration, 
Neutral  Axis 
Parallel  with 
Center  line  of 
web. 

Section 
Modulus, 
Neutral  Axis 
Perpendicular 
to  web  at 
Center. 

Coefficient 
of  Strength  for 
Fibre  Stress  of 
16,0001bs. 
per  sq.  in. 
used  for 
Buildings. 

-A*  . 

C  -t~>  -*J  »—  '    C    tn 

o  MCOo"*,8  % 

iJllfif 

o^E-H  «  3PQ 

°l° 

Distance 
Between 
Channels 
Required  to 
make  Radii  of 
Gyration  equal 

Distance  of 
Center  of 
Gravity  from 
Outside  of  web. 

Section  Index. 

r' 

S 

C 

C' 

X 

.912 

41.7 

444500 

347300 

9.50 

0.794 

Cl 

.805 

21.4 

227800 

178000 

7.67 

0.704 

C2 

.718 

13.4 

142700 

111500 

6.33    . 

0.639 

C3 

.674 

10.5 

112200 

87600 

5.63 

0.607 

C4 

.630 

8.1 

86100 

67300 

4.94 

0.576 

C5 

.586 

6.0 

66800 

52200 

4.22 

0.546 

C6 

.542 

4.3 

46200 

36100 

3.52 

0.517 

C7 

.498 

3.0 

31600 

24700 

2.79 

C.489 

C8 

.453 

1.9 

20200 

15800 

2.06 

0.464 

C9 

.409 

1.1 

11600 

9100 

1.31 

0.443 

C72 

For  each  of  the  above  tables: 


58 


REINFORCED    CONCRETE. 


TABLE  XXXI. — PROPERTIES  OF  STANDARD  CARNEGIE  ANGLES. 
Angles  with  unequal  legs. 


1 

2 

3 

4 

5 

6 

7 

Weight 

Area  of 

Perpendicular  Distance 
from  Center  of  Gravity 

Section 

Size 
in 

Thickness 
in 

per 
Foot 

Section 

in 

to  Back  of  Flange. 

Index. 

Inches. 

Inches. 

in. 
Pounds 

Square 
Inches. 

To  Back  of 
Longer 

To  Back  o£ 
Shorter 

Flange. 

Flange. 

A  89 

6  x 

1 

30.6 

9.00 

1.17 

2.17 

A  91 

6  x 

T! 

28.9 

8.50 

1.14 

2.14 

A160 

6  x 

I 

27.2 

7.99 

1.12 

2.12 

A161 

6  x 

a 

25.4 

7.47 

1.10 

2.10 

A162 

6  x 

i 

23.6 

6.94 

1.08 

2.08 

A163 

6  x 

21.8 

6.41 

1.06 

2.06 

A164 

6  x 

i 

20.0 

5.86 

1.03 

2.03 

A165 

6  x 

9 

18.1 

5.31 

1.01 

2.01 

A166 

6  x 

I 

16.2 

4.75 

0.99 

1.99 

A167 

6x4 

?7 

14.3 

4.18 

0.96 

1.96 

A168 

6x4 

12.3 

3.61 

0.94 

1.94 

A  92 

6  x  3J 

1 

28.9 

8.50 

1  01 

2.26 

A  93 

6  x  »• 

l| 

27.3 

8.03 

0.99 

2.24 

A169 

6x3 

1*3 

25.7 

7.55 

0.97 

2.22 

A170 

6x3 

24.0 

7.06 

0.95 

2.20 

A171 

6  x  & 

| 

22.4 

6.56 

0.93 

2.18 

A172 

6x3 

11 

20.6 

6.06 

0.90 

2.15 

A173 

6x3 

| 

18.9 

5.55 

0.88 

2.13 

A174 

6  x  3J 

9 

17.1 

5.03 

0.86 

2.11 

A175 

6x3 

I 

15.3 

4.50 

0.83 

2.08 

A176 

6x3 

yg 

13.5 

3.97 

0.81 

2.06 

A177 

6  x  # 

f 

11.7 

3.42 

0.79 

2.04 

A187 

5  x  3J 

i 

22.7 

6.67 

1.04 

1.79 

A  188 

5  x  3J 

TS 

21.3 

6.25 

1.02 

1.77 

A189 

5  x  3= 

I 

19.8 

5.81 

1.00 

1.75 

A190 

5x3 

18.3 

5.37 

0.97 

1.72 

A191 

5x3 

jj 

16.8 

4.92 

0.95 

1.70 

A192 

5x3 

9 

15.2 

4.47 

0.93 

1.68 

A193 

5x3 

X 

13.6 

4.00 

0.91 

1.66 

A  194 

5x3' 

r 

12.0 

3.53 

0.88 

1.63 

A195 

5x3; 

| 

10.4 

3.05 

0.86 

1.-61 

A  96 

5  x  3J 

I68 

8.7 

2.56 

0.84 

1.59 

A196 

5  x  3 

11 

19.9 

5.84 

0.86 

1.86 

A197 

5x3 

1 

18.5 

5.44 

0.84 

.84 

A198 

5x3 

18 

17.1 

5.03 

0.82 

.82 

A199 

5x3 

f 

15.7 

4.61 

0.80 

.80 

A200 

5x3 

ft 

14.3 

4.18 

0.77 

.77 

A201 
A202 

5x3 
5x3 

f 

12.8 
11.3 

3.75 
3.31 

0.75 
0.73 

75 
.73 

A203 

5x3 

f 

9.8 

2.86 

0.70 

.70 

A280 

5x3 

A 

8.2 

2.40 

0.68 

.68 

MATERIALS  AND  MACHINES. 


59 


TABLE  XXXi.     (Continued).— PROPERTIES  OP  STANDARD  CARNEGIE  ANGLES. 
Angles  with  unequal  lees. 


8 

9 

10                   11 

12 

13 

14 

15 

Moment 

D£  Inertia. 

Section  Modulus. 

Radii 

of  Gyratic 

>n. 

I 

S 

r 

Neutral 

Neutral 

Neutral 

Neutral 

Neutral 

Neutral 

Sec- 

Axis 

Axis 

Axis 

Axis 

Axis 

Axis 

Least 

tion 

Parallel  to 

Parallel  to 

Parallel  to 

Parallel  to 

Paral'l  to 

Paral'l  to 

Radi- 

Index 

Longer 

Shorter 

Longer 

Shorter 

Longer 

Shorter 

us. 

Flange. 

Flange. 

Flange. 

Flange. 

Flange. 

Flange. 

10.75 

30.75 

3.79 

8.02 

1.09 

1.85 

0.85 

A  89 

10.26 

29.26 

3.59 

7.59 

1.10 

1.86 

0.85 

A  91 

9.75 

27.73 

3.39 

7.15 

1.11 

1.86 

0.86 

A160 

9.23 

26.15 

3.18 

6.70 

1.11 

1.87 

0.86 

A161 

8.68 

24.51 

2.97 

6.25 

1.12 

1.88 

0.86 

A  162 

8.11 

22.82 

2.76 

5.78 

1.13 

1.89 

0.86 

A  163 

7.52 

21.07 

2.54 

5.31 

1.13 

1.90 

0.86 

A  164 

6.91 

19.26 

2.31 

4.83 

1.14 

1.90 

0.87 

A165 

6.27 

17.40 

2.08 

4.33 

1.15 

1.91 

0.87 

A  166 

5.60 

15.46 

1.85 

3.83 

1.16 

1.92 

0.87 

A  167 

4.90 

13.47 

1.60 

3.32 

1.17 

1.93 

0.88 

A168 

7.21 

29.24 

2.90 

7.83 

0.92 

1.85 

0.74 

A  92 

6.88 

27.84 

2.74 

7.41 

0.93 

1.86 

0.74 

A  93 

6.55 

26.38 

2.59 

6.98 

0.93 

1.87 

0.75 

A169 

6.20 

24.89 

2.43 

6.55 

0.94 

1.88 

0.75 

A170 

5.84 

23.34 

2.27 

6.10 

0.94 

1.89 

0.75 

A171 

5.47 

21.74 

2.11 

5.65 

0.95 

1.89 

0.75 

A172 

5.08 

20.08 

.94 

5.19 

0.96 

1.90 

0.75 

A  173 

4.67 

18.37 

.77 

4.72 

0.96 

1.91 

0.75 

A  174 

4.25 

16.59 

.59 

4.24 

0.97 

1.92 

0.76 

A175 

3.81 

14,76 

.41 

3.75 

0.98 

1.93 

0.76 

A176 

3.34 

12.86 

.23 

3.25 

0.99 

1.94 

0.77 

A177 

6.21 

15.67 

2.52 

4.88 

0.96 

1.53 

0.75 

A187 

5.89 

14.81 

2.37 

4.58 

0.97 

1.54 

0.75 

A  188 

5.55 

13.92 

2.22 

4.28 

0.98 

1.55 

0.75 

A  189 

5.20 

12.99 

2.06 

3.97 

0.98 

1.56 

0.75 

A  190 

4.83 

12.03 

1.90 

3.65 

0.99 

1.56 

0.75 

A191 

4.45 

11.03 

1.73 

3.32 

1.00 

1.57 

0.75 

A  192 

4.05 

9.99 

1.56 

2.99 

1.01 

1.58 

0.75 

A193 

3.63 

8.90 

1.39 

2.64 

1.01 

1.59 

0.76 

A  194 

3.18 

7.78 

1.21 

2.29 

1.02 

1.60 

0.76 

A  195 

2  72 

6.60 

1.02 

1.94 

1.03 

1.61 

0.76 

A  96 

3.'71 

13.98 

.74 

4.45 

0.80 

1.55 

0.64 

A196 

3.51 

13.15 

.63 

4.16 

0.80 

1.55 

0.64 

A  197 

3.29 

12.28 

.51 

3.86 

0.81 

1.56 

0.64 

A  198 

3.06 

11.37 

.39 

3.55 

0.82 

1.57 

0.64 

A  199 

2.83 

10.43 

.27 

3.23 

0.82 

1.58 

0.65 

A200 

2.58 

9.45 

.15 

2.91 

0.83 

1.59 

0.65 

A201 

2.32 

8.43 

.02 

2.58 

0.84 

1.60 

0.65 

A202 

2.04 

7.37 

0.89 

2.24 

0.84 

1.61 

0.65 

A203 

1.75 

6.26 

0.75 

1.89 

0.85 

1.61 

0.66     A280 

60 


REINFORCED   CONCRETE. 


TABLE  XXXII. — PROPERTIES  OF  STANDARD  CARNEGIE  ANGLES. 
Angles  with  unequal  legs. 


1 

2 

3 

4 

5 

6 

7 

Perpendicular  Distance 

Section 

Size 

in 

Thickness 
in 

Weight 
Foot 

Area  of 
Section 
in 

from  Center  of  Gravity 
to  Back  of  Flange. 

Index. 

Inches 

Inches. 

in 
Pounds. 

Square 
Inches. 

To  Back  of 
Longer 

To  Back  cl 
Shorter 

Flange. 

Flange. 

A220 

4x3 

u 

17.1 

5.03 

0.94 

.44 

A221 

4x3 

I 

16.0 

4.69 

0.92 

.42 

A222 

4x3 

IB 

14.8 

4.34 

0.89 

.39 

A223 

4x3 

f 

13.6 

3.98 

0.87 

.37 

A224 

4x3 

I93 

12.4 

3.62 

0.85 

.35 

A225 

4x3 

^ 

11.1 

3.25 

0.83 

.33 

A226 

4x3 

/3 

9.8 

2.87 

0.80 

.30 

A227 

4x3 

1 

8.5 

2.48 

0.78 

.  28 

A228 

4x3 

1 
IS 

7.2 

2.09 

0.76 

.26 

A229 

33 

x  3 

u 

15.8 

4.62 

0.98 

.23 

A230 

3 

x  3 

i 

14.7 

4.31 

0.96 

.21 

A231 

3 

x  3 

18 

13.6 

4.00 

0.94 

.19 

A232 

x  3 

I 

12.5 

3.67 

0.92 

.17 

A233 

si 

x  3 

11.4 

3.34 

0.90 

.15 

A234 

3: 

x  3 

X 

10.2 

3.00 

0.88 

.13 

A235 

ft 

x  3 

TR 

9.1 

2.65 

0.85 

.10 

A236 

x  3 

7.9 

2.30 

0.83 

.08 

A237 

3: 

x  3 

13 

6.6 

1.93 

0.81 

.06 

A238 

3; 

x  2j 

11 

12.5 

3.65 

0.77 

.27 

A239 

i 

x  2- 

| 

11.5 

3.36 

0.75 

.25 

A240 

3« 

x  2< 

IB 

10.4 

3.06 

0.73 

.23 

A241 

i 

x  2i 

I 

9.4 

2.75 

0.70 

.20 

A242 

8i 

x  2i 

T?8 

8.3 

2.43 

0.68 

.18 

A243 

8j 

X  2; 

| 

7  2 

2.11 

0.66 

.16 

A244 

3 

x  2\ 

JL 

6.1 

1.78 

0.64 

.14 

A245 

3; 

i 

4.9 

1.44 

0.61 

.11 

A252 

3  x  23 

I98 

9.5 

2.78 

0.77 

.02 

A253 

3  x  2> 

i 

8.5 

2.50 

0.75 

.00 

A254 

3  x  2> 

A 

7.6 

2.22 

0.73 

0.98 

A255 
A256 
A257 

3  x  % 
3  x  % 
3x2; 

1 

6.6 
5.6 
4.5 

1.92 
1.62 
1.31 

0.71 
0.68 
0.66 

0.96 
0.93 
0.91 

A264 

2*  x  2 

1 

6.8 

2.00 

0.63 

0.88 

A265 

2 

x  2 

6.1 

1.78 

0.60 

0.85 

A266 

2J 

r  x  2 

1* 

5.3 

1.55 

0.58 

0.83 

A267 

2J 

x  2 

T3 

4.5 

1.31 

0.56 

0.81 

A268 

2 

r  x  2 

3.7 

1.06 

0.54 

0.79 

A269 

r  x  2 

_ 

2.8 

0.81 

0.51 

0.76 

MATERIALS  AND  MACHINES. 


61 


TABLE  XXXII.    (Continued). — PROPERTIES  OF  STANDARD  CARNEGIE  ANGLES. 
Angles  with  unequal  legs. 


8 

9 
^ 

10                   11 

12 

13 

14 

15 

Moment  c 

)f  Inertia. 

Section  Modulus. 

Radii 

of  Gyratic 

n. 

I 

S 

r 

Neutral 

Neutral 

Neutral 

Neutral 

Neutral 

Neutral 

Sec- 

Axis 

Axis 

Axis 

Axis 

Axis 

Axis 

Least 

tion 

Parallel  to 

Parallel  to 

Parallel  to 

Parallel  to 

Paral'l  to 

Paral'l  to 

Radi- 

Index 

Longer 

Shorter 

Longer 

Shorter 

Longer 

Shorter 

us. 

Flange. 

Flange. 

Flange. 

Flange. 

Flange. 

-  Flange. 

3.47 

7.34 

1.68 

2.87 

0.83 

.21 

0.64 

A220 

3.28 

6.93 

1.57 

2.68 

0.84 

.22 

0.64 

A221 

3.08 

6.49 

1.46 

2.49 

0.84 

.22 

0.64 

A222 

2.87 

6.03 

1.35 

2.30 

0.85 

.23 

0.64 

A223 

2.66 

5.55 

1.23 

2.09 

0.86 

.24 

0.64 

A224 

2.42 

5.02 

1.12 

1.89 

0.86 

.25 

0.64 

A225 

2.18 

4.52 

0.99 

1.68 

0.87 

.25 

0.64 

A226 

1.92 

3.96 

0.87 

1.46 

1.88 

.26 

0.64 

A227 

1.65 

3.38 

0.74 

1.23 

0.89 

.27 

0.65 

A228 

3.33 

4.98 

1.65 

2.20 

0.85 

1.04 

0.62 

A229 

3.15 

4.70 

1.54 

2.05 

0.85 

1.04 

0.62 

A230 

2.96 

4.41 

1.44 

1.91 

0.86 

1.05 

0.62 

A231 

2.76 

4.11 

1.33 

1.76 

0.87 

1.06 

0.62 

A232 

2.55 

3.79 

1.21 

1.61 

0.87 

1.07 

0.62 

A233 

2.33 

3.45 

1.10 

1.45 

0.88 

1.07 

0.62 

A234 

2.09 

3.10 

0.98 

1.29 

0.89 

1.08 

0.62 

A235 

1.85 

2.72 

0.85 

1.13 

0.90 

1.09 

0.62 

A236 

1.58 

2.33 

0.72 

0  96 

0.90 

1.10 

0.63 

A237 

1.72 

4.13 

0.99 

1.85 

0.67 

.06 

0.53 

A233 

1.61 

3.85 

0.92 

1.71 

0.69 

.07 

0.53 

A239 

1.49 

3.55 

0.84 

1.56 

0.70 

.08 

0.53 

A240 

1.36 

3.24 

0.76 

1.41 

0.70 

.09 

0.53 

A241 

1.23 

2.91 

0.68 

1.26 

0.71 

.09 

0.54 

A242 

1.09 

2.56 

0.59 

1.09 

0.72 

.10 

0.54 

A243 

0.94 

2.19 

0.50 

0.93 

0.73 

.11 

0.54 

A244 

0.78 

1.80 

0.41 

0.75 

0.74 

.12 

0.54 

A245 

1.42 

2.28 

0.82 

1.15 

0.72 

0.91 

0.52 

A252 

1.30 

2.08 

0.74 

1.04 

0.72 

0.91 

0.52 

A253 

1.18 

1.88 

0.66 

0.93 

0.73 

0.92 

0.52 

A254 

1.04 

1.66 

0.58 

0.81 

0.74 

0.93 

0.52 

A255 

0.90 

1.42 

0.49 

0.69 

0.74 

0.94 

0.53 

A256 

0.74 

1.17 

0.40 

0.56 

0.75 

0.95 

0.53 

A257 

0.64 

1.14 

0.46 

0.70 

0.56 

0.75 

0.42 

A264 

0.58 

1.03 

0.41 

0.62 

0.57 

0.76 

0.42 

A265 

0.51 

0.91 

0.36 

0.55 

0.58 

0.77 

0.42 

A266 

0.45 

0.79 

0.31 

0.47 

0.58 

0.78 

0.42 

A267 

037 

0.65 

0.25 

0.38 

0.59 

0.78 

0.42 

A268 

0.29 

0.51 

0.20 

0.29 

0.60 

0.79 

0.43 

A269 

62 


REINFORCED    CONCRETE. 


TABLE  XXXIII. — PROPERTIES  OF  STANDARD  CARNEGIE  ANGLES. 
Angles  with  equal  legs. 


1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

"o  ° 

60 

& 

B 

-  o 

"rtM 

8 

J3 

c 

S3  3  j. 

.3  1*2 

.1 

.p 

>>§>>- 

O 

i 

1 

| 

C 

I 

'£J3 

5    *§ 

Jjjlig 

.33 

l! 

|.al| 

*o 

o 

C 

•«H 

RT§ 

33 

l^*j 

Io<l2£ 

_J< 

•£«< 

^2^ 

G 

O 

1 

Size  in  I 

1 

O 

H 

!§ 

K 

III 

.a  2,2 

QOfe 

Moment 
Neutral 
Center  o 
Parallel 

§1 
11 

|| 

^S«J 

I 

S 

r 

J    ^0(3 

A113 

8x8 

If 

56.9 

16.73 

2.41 

97.97 

17.53 

2.42 

.55 

A112 

8x8 

ITB 

54.0 

15.87 

2.39 

93.53 

16.67 

2.43 

.56 

Alll 

8x8 

1 

51.0 

15.00 

2.37 

88.98 

15.80 

2.44 

.56 

A110 

8x8 

U 

48.1 

14.12 

2.34 

84.33 

14.91 

2.44 

.56 

A109 

8x8 

¥ 

45.0 

13.23 

2.32 

79.58 

14.01 

2.45 

.57 

A108 

8x8 

ii 

42.0 

12.34 

2.30 

74.71 

13.11 

2.46 

.57 

A107 

8x8 

1 

38.9 

11.44 

2.28 

69.74 

12.18 

2.47 

.57 

A106 

8x8 

35.8 

10.53 

2.25 

64.64 

11.25 

2.48 

.58 

A105 

8x8 

f 

32.7 

9.61 

2.23 

59.42 

10.30 

2.49 

.58 

A104 

8x8 

9 

29.6 

8.68 

2.21 

54.09 

9.34 

2.50 

.58 

A103 

8x8 

i 

26.4 

7.75 

2.19 

48.63 

8.37 

2.50 

.58 

A86 

6x6 

1 

37.4 

11.00 

.86 

35.46 

8.57 

.80 

.16 

A87 

6x6 

11 

35.3 

10.37 

.84 

33.72 

8.11 

.80 

.16 

Al 

6x6 

} 

33.1 

9.74 

.82 

31.92 

7.64 

.81 

.17 

A2 

6x6 

TB 

31.0 

9.09 

.80 

30.06 

7.15 

.82 

.17 

A3 

6x6 

¥ 

28.7 

8.44 

.78 

28.15 

6.66 

.83 

.17 

A4 

6x6 

TB 

26.5 

7.78 

.75 

26.19 

6.17 

.83 

.17 

A5 

6x6 

¥ 

24.2 

7.11 

.73 

24.16 

5.66 

.84 

.18 

A6 

6x6 

TB 

21.9 

6.43 

.71 

22.07 

5,14 

.85 

1.18 

A7 

6x6 

19.6 

5.75 

.68 

19.91 

4.61 

.86 

1.18 

A8 

6x6 

TB 

17.2 

5.06 

.66 

17.68 

4.07 

.87 

1.19 

A88 

6x6 

14.9 

4.36 

.64 

15.39 

3.53 

.88 

1.19 

A18 

4x4 

11 

19.9 

5.84 

.29 

8.14 

3.01 

.18 

0.77 

A19 

4x4 

? 

18.5 

5.44 

.27 

7.67 

2.81 

.19 

0.77 

A20 

4x4 

17.1 

5.03 

.25 

7.17 

2.61 

.19   ' 

0.77 

A21 

4x4 

i 

15.7 

4.61 

.23 

6.66 

2.40 

.20 

0.77 

A22 

4x4 

14.3 

4.18 

.21 

6.12 

2.19 

.21 

0.78 

A23 

4x4 

12.8 

3.75 

.18 

5.56 

1.97 

.22 

0.78 

A24 

4x4 

11.3 

3.31 

.16 

4.97 

1.75 

.23 

0.78 

A25 

4x4 

¥ 

9.8 

2.86 

.14 

4.36 

1.52 

.23 

0.79 

A90 

4x4 

8.2 

2.40 

.12 

3.71 

1.29 

.24 

0.79 

A26 

31x3; 

13 

17  1 

5.03 

.17 

5.25 

2.25 

.02 

0.97 

A27 

31x3' 

• 

16.0 

4.69 

.15 

4.96 

2.11 

.03 

0.67 

A28 

31x3i 

TO 

14.8 

4.34 

.12 

4.65 

1.96 

.04 

0.67 

A29 

31x3i 

1 

13.6 

3.98 

1.10 

4.33 

1.81 

.04 

0.67 

A30 

31x3' 

T9B 

12.4 

3.62 

1.08 

3.99 

1.65 

.05 

0.68 

A31 

31x31 

X 

11.1 

3.25 

1.06 

3.64 

1.49 

.06 

0.68 

A32 

31x21 

Tff 

9.8 

2.87 

1.04 

3.26 

1.32 

.07 

0.68 

A33 

31x31 

8.5 

2.48 

1.01 

2.87 

1.15 

.07 

0.69 

A99 

3ix3i 

" 

7.2 

2.09 

0.99 

2.45 

0.98 

.08 

0.69 

MATERIALS  AND  MACHINES. 


63 


TABLE  XXXIV. — PROPERTIES  OF  STANDARD  CARNEGIE  ANGLES 
Angles  with  equal  'legs. 


1 

2 

3 

4 

5 

6 

7 

V 

8 

9 

10 

Section  Index. 

Size  in  Inches. 

Thickness  in  Inches. 

1 

fc«.' 

Area  of  Section,  in 
Square  Inches. 

Distance  of  Center  of 
Gravity  from  Back  of 
Flange,  in  Inches. 

Moment  of  Inertia, 
Neutral  Axis  through 
'-'Center  of  Gravity 
Parallel  to  Flange. 

^Section  Modulus, 
Neutral  Axis  as  before. 

Radius  of  Gyration, 
M  Neutral  Axis  as  before. 

Least  Radius  of  Gyra'n, 
H  Neutral  Axis  through 
^Center  of  Gravity 
at  45°  to  Flanges. 

A34 

5x3 

| 

11.5 

3.36 

0.98 

2.62 

1.30 

0.88 

0.57 

A35 

5x3 

i 

10.4 

3.06 

0.95 

2.43 

1.19 

0.89 

0.58 

A36 

5x3 

i 

9.4 

2.75 

0.93 

2.22 

1.07 

0.90 

0.58 

A37 

5x3 

T7B 

8.3 

2.43 

0.91 

1.99 

0.95 

0.91 

0.58 

A38 

5x3 

• 

7.2 

2.11 

0.89 

1.76 

0.83 

0.91 

0.58 

A39 

5x3 

6 

6.1 

1.78 

0.87 

1.51 

0.71 

0.92 

0.59 

A40 

5x3 

i 

4.9 

1.44 

0.84 

1.24 

0.58 

0.93 

0.59 

A46 

2^ 

x2 

1 

j 

7.7 

2.25 

0.81 

1.23 

0.73 

0.74 

0.47 

A47 

2 

x2 

?| 

6.8 

2.00 

0.78 

1.11 

0.65 

0.74 

0.48 

A48 

2 

x2 

5.9 

1.73 

0.76 

0.98 

0.57 

0.75 

0.48 

A49 

2 

x2 

5.0    . 

1.47 

0.74 

0.85 

0.48 

0.76 

0.49 

A50 

2 

x2 

? 

4.1 

1.19 

0.72 

0.70 

0.40 

0.77 

0.49 

A100 

2 

x2 

3.1 

0.90 

0.69 

0.55 

0.30 

0.78 

0.49 

A56 

l 

>x2 

$i 

5.3 

1.56 

0.66 

0.54 

0.40 

0.59 

0.39 

A57 

x2 

4.7 

1.36 

0.64 

0.48 

0.35 

0.59 

0.39 

A58 

i 

>x2 

4.0 

1.15 

0.61 

0.42 

0.30 

0.60 

0.39 

A59 

\ 

'x2 

3.2 

0.94 

0.59 

0.35 

0.25 

0.61 

0.39 

AGO 

( 

x2 

T8 

2.5 

0.72 

0.57 

0.28 

0.19 

0.62 

0.40 

A61 

xl 

7 

4.6 

1.30 

0.59 

0.35 

0.30 

0.51 

0.33 

AG2 

xl 

V 

4.0 

1.17 

0.57 

0.31 

0.26 

0.51 

0.34 

A63 

xl 

6 

3.4 

1.00 

0.55 

0.27 

0.23 

0.52 

0.34 

A64 

xl 

1 

2.8 

0.81 

0.53 

0.23 

0.19 

0.53 

0.34 

A65 

xl 

A 

2.2 

0.62 

0.51 

0.18 

0.14 

0.54 

0.35 

A66 

xl 

1 

3.4 

0.99 

0.51 

0.19 

0.19 

0.44 

0.29 

A67 

xl 

ft 

2.9 

0.84 

0.49 

0.16 

0.162 

0.44 

0.29 

ACS 

xl 

I 

2.4 

0.69 

0.47 

0.14 

0.134 

0.45 

0.29 

AG9 

xl 

1.8 

0.53 

0.44 

0.11 

0.104 

0.46 

0.29 

A  102 

xl 

Y 

1.3 

0.36 

0.42 

0.08 

0.070 

0.46 

0.30 

A70 

i 

xl 

TBB 

2.4 

0.69 

0.42 

0.09 

0.109 

0.36 

0.23 

A71 

xl 

1 

2.0 

0.56 

0.40 

0.077 

0.091 

0.37 

0.24 

A72 

xl 

1.5 

0.43 

0.38 

0.061 

0.071 

0.38 

0.24 

A73 

xl 

1.1 

0.30 

0.35 

0.044 

0.049 

0.38 

0.25 

A78 

] 

xl 

J 

1.5 

0.44 

0.34 

0.037 

0.056 

0.29 

0.19 

A79 

] 

xl 

A 

1.2 

0.34 

0.32 

0.030 

0.044 

0.30 

0.19 

A80 

] 

xl 

T 

0.8 

0.24 

0.30 

0.022 

0.031 

0.31 

0.20 

A83 

X 

0.9 

0.25 

0.26 

0.012 

0.024 

0.22 

0.16 

A84 

X 

0.6 

0.17 

0.23 

0.009 

0.017 

0.23 

0.17 

64  REINFORCED    CONCRETE. 

TABLE  XXXV. — AREA  AND  CIRCUMFERENCE  OF  CIRCLES. 


Diameter, 

Area. 

Circumference 

Decimals 
of  a  foot. 

Ins.  and 
fract'ns 

Ins  and 
decimals. 

Decimals 
of  a  sq.  ft. 

Sq.  ins. 
decimals. 

Decimals 
of  a  foot. 

Ins.  and 
decimals. 

.00260 

.. 

.03125 

.000005 

.00077 

.0082 

.09818 

.00521 

i 

.0625 

.000021 

.00307 

.0164 

.  19635 

.00781 

& 

.09375 

.000048 

.00690 

.0245 

.29452 

.01042 

i 

.125 

.000085 

.01227 

.0327 

.39270 

.01302 

!56Z 

.15625 

.000133 

.01917 

.0409 

.49087 

.01562 

.1875 

.000192 

.02761 

.0491 

.58905 

.01823 

A 

.21875 

.000261 

.03758 

.0573 

.68722 

.02083 

| 

.25 

.000341 

.04909 

.0654 

.78540 

.02344 

.28125 

.000431 

.06213 

.0736 

.88357 

.02604 

6 

.3125 

.000533 

.07670 

.0818 

.98175 

.02865 

si 

.34375 

.000644 

.09281 

.0900 

1.0799 

.03125 

1 

.375 

.000767 

.11045 

.0982 

1.1781 

.03385 

£3 

.40625 

.000900 

.12962 

.1064 

1.2763 

.03646 

TB 

.4375 

.001044 

.15033 

.1145 

1.3744 

.03906 

II 

.46875 

.001198 

.17257 

.1227 

1.4726 

.04167 

I 

.50 

.001363 

.19635 

.1309 

.5708 

.04427 

hi 

.53125 

.001539 

.22166 

.1391 

.6690 

.04688 

.5625 

.001726 

.24850 

.1473 

.7671 

.04948 

.59375 

.001923 

.27688 

.1554 

.8653 

.05208 

.625 

.002130 

.30680 

.1636 

.9635 

.05469 

H 

.65625 

.002349 

.33824 

.1718 

2.0617 

.05729 

|| 

.6875 

.002578 

.37122 

.1800 

2.1598 

.05990 

.71875 

.002817 

.40574 

.1882 

2.2580 

.06250 

f 

.75 

.003068 

.44179 

.1963 

2.3562 

.06510 

.78125 

.003329 

.47937 

2045 

2.4544 

.06771 

13 

.8125 

.003604 

.51849 

.2127 

2.5525 

.07031 

li 

.84375 

.003883 

.55914 

.2209 

2.6507 

.07292 

1 

.875 

.004176 

.60132 

.2291 

2.7489 

.07552 

§1 

.90625 

.004479 

.64504 

.2373 

2.8471 

.07813 

TB 

.9375 

.004793 

.69029 

.2454 

2.9452 

.08073 

ii 

.96875 

.005118 

.73708 

.2536 

3.0434 

.0833 

1 

.0000 

.005454 

.7854 

.2618 

3.1416 

.0,859 

A 

.03125 

.005800 

.8353 

.2700 

3.2398 

.  0*885 

X 

.0625 

.006157 

.8866 

.2782 

3.3379 

.0911 

.09375 

.006524 

.9396 

.2863 

3.4361 

.0938 

i 

.125 

.006902 

.9940 

.2945 

3.5343 

.0964 

/i 

.15625 

.007291 

.0500 

.3027 

3.6325 

.0990 

IB 

.1875 

.007691 

.1075 

.3109 

3.7306 

.1016 

g 

.21875 

.008101 

.1666 

.3191 

3.8288 

.1042 

1 

.25 

.008522 

.2272 

.3272 

3.9270 

.1068 

39Z 

.28125 

.008953 

.2893 

.3354 

4.0252 

.1094 

i6g 

.3125 

.009395 

.3530 

.3436 

4.1233 

.1120 

y 

.34375 

.009848 

.4182 

.3518 

4.2215 

.1146 

f 

.375 

.010311 

1.4849 

.3600 

4.3197 

.1172 

a 

.40625 

.010785 

1.5532 

.3682 

4.4179 

.1198 
.1224 

a 

.4375 
.46875 

.011270 
.012197 

1.6230 
1.6943 

.3763 
.3845 

4.5160 
4.6142 

MATERIALS  AND  MACHINES.  65 

TABLE  XXXV.    (Continued).— AREA  AND  CIRCUMFERENCE  OF  CIRCLES. 


Diameter. 

Area. 

Circumference 

Decimals 
of  a  foot. 

Ins.  and 
fract'ns 

In.  and 
decimals. 

Decimals 
of  a  sq.  ft. 

Sq.  ins. 
decimals. 

Decimals 
of  a  foot. 

Ins.  and 
decimals. 

.1250 

n 

1.50 

.01227 

1.7671 

.3927 

4.7124 

.1276 

ii 

1.53125 

.01279 

1.8415 

.4009 

4.8106 

.1302 

T9B 

1.5625 

.01331 

1.9175 

.4091 

4.9087 

.1328 

H 

1.59375 

.01385 

1.9949 

.4172 

5.0069 

.1354 

f 

1.625 

.01440 

2.0739 

.4254 

5.1051 

.1380 

H 

1.G5625 

.01493 

2.1545 

.4336 

5.2033 

.1406 

\ls 

1.6875 

.01553 

2.2365 

.4418 

5.3014 

.1432 

ii 

1.71875 

.01611 

2.3201 

.4500 

5.3996 

.1458 

1 

1.75 

.01670 

2.4053 

.4581 

5.4978 

.1484 

1.78125 

.01730 

2.4920 

.4663 

5.5960 

.1510 

IB 

1.8125 

.01792 

2.5802 

.4745 

5.6941 

.1536 

32 

1.84375 

.01854 

2.9699 

.4827 

5.7923 

.1563 

J 

1.875 

•  .01917 

2.7612 

.4909 

5.8905 

.1589 

HI 

1.90625 

.01982 

2.8540 

4991 

5.9887 

.1615 

T8 

1.9375 

.02047 

2.9483 

.5072 

6.0868 

.1642 

Ii 

1.96875 

.02114 

3.0442 

.5154 

6.1850 

.1667 

2 

2.00 

.02182 

3.1416 

.5236 

6.2832 

.1719 

TO 

2.0625 

.02320 

3.3410 

.5400 

6.4795 

.1771 

2.125 

.02463 

3.5466 

.5563 

6.6759 

.1823 

13B 

2.1875 

.02610 

3.7583 

.5727 

6.8722 

.1875 

2.25 

.02761 

3.9761 

.5890 

7.0686 

.1927 

TB3 

2.3125 

.02917 

4.2000 

.6054 

7.2649 

.1979 

| 

2.375 

.03076 

4.4301 

.6218 

7.4613 

.2031 

T?8 

2.4375 

.03240 

4.6664 

.6381 

7.6576 

.2083 

i 

2.50 

.03409 

4.9087 

.6545 

7.8540 

.2135 

T9B 

2.5625 

.03581 

5.1572 

.6709 

8.0503 

.2187 

? 

2.625 

.03758 

5.4119 

.6872 

8.2467 

.2240 

2.6875 

.03939 

5.6727 

.7036 

8.4430 

.2292 

• 

2.75 

.04124 

5.9396 

.7199 

8.6394 

.2344 

13 

2.8125 

.04314 

6.2126 

.7363 

8.8357 

.2396 

J 

2.875 

.0^508 

6.4918 

.7527 

9.0321 

.2448 

il 

2.9375 

.04706 

6.7771 

.7690 

9.2284 

.2503 

3^ 

3.00 

.04908 

7.0686 

'.7854 

9.4248 

.2552 

3.0625 

.05115 

7.3662 

.8018 

9.6211 

.2o04 

X 

3.125 

.05326 

7.6699 

.8181 

§.8175 

.2856 

3 

3.1875 

.0*541 

7.9798 

.8345 

10.014 

.2708 

| 

3.25 

.05761 

8.2958 

.8508 

10.210 

.2760 

•fa 

3.3125 

.05984 

8.6179 

.8672 

10.407 

.2812 

3.375 

.06212 

8.9462 

.8836 

10.603 

.2865 

T8 

3.4375 

.06444 

9.2806 

.8999 

10.799 

.2917 

* 

3.50 

.06681 

9.6211 

.9163 

10.996 

.2969 

3.5625 

.06922 

9.9678 

.9327 

11.192 

.3021 

3.625 

.07167 

10.321 

.9490 

11.388 

.3073 

u 

3.6875 

.07416 

10.680 

.9654 

11.585 

.3125 

i 

3.75 

.07669 

10.045 

.9817 

11.781 

.3177 

9 

3.8125 

.07927 

11.416 

.9981 

11.977 

.3229 

1 

3.875 

.08189 

11.793 

1.0145 

12.174 

.3281 

il 

3.9375 

.08456 

12.177 

1.0308 

12.370 

.3333 

4 

4.00 

.08726 

12.566 

1.0472 

12.566 

66  REINFORCED    CONCRETE. 

TABLE  XXXVI. — PROPERTIES  OF  VARIOUS  SECTIONS. 


SECTION. 


Moment  of 

Inertia. 

I 


Section  Modulus 


_ 
12 


36 


__ 
12 


^  0.0491J* 


12 


12 


24 


32 


0.098 


xx  is  the  position  of  neutral  axis. 

n  and  n'  are  the  distances  from  the  neutral  axis  to  most  remote  fibers  of  the 
section;    n  being  the  greater. 


CHAPTER   II. 

DESIGN  AND  CONSTRUCTION  OF  BUILDINGS. 
GENERAL  DISCUSSION. 

Reinforced  concrete  is  used  for  nearly  every  type  of  build- 
ing. The  variety  of  designs  employed  is  so  great  that  the 
subject  will  be  considered  here  in  only  a  general  way.  In 
all  designing  it  is  necessary  to  figure  on  the  strength  at- 
tained by  the  concrete  at  the  time  the  molds  are  removed. 
For  instance,  when  molds  must  be  removed  in  48  hours,  it 
is  necessary  to  design  a  section  that  will  have  the  requisite 
strength  in  48  hours;  where  molds  may  remain  for  28  days, 
early  strength  is  not  required. 

General  Assumptions  Made  in  Design. — Before  designing, 
certain  assumptions  must  be  made  in  order  to  eliminate  some 
of  the  variables  entering  into  reinforced  concrete  construc- 
tion. The  assumptions  usually  made  in  the  United  States 
to  date  are  as  follows: 

(1)  Sections    plane    before    bending    remain    plane    after 
bending,  at  least  within  the  limit  of  elasticity  of  the  steel. 

(2)  Stresses  in  sections  subjected  to   bending  are  com- 
puted assuming  that  elongations  vary  with  the  distance  from 
the  neutral  axis. 

(3)  The  union  between  the  steel  and  the  concrete  is  suf- 
ficient to  cause  the  two  materials  to  act  as  one  material,  the 
unit  value  of  adhesion  being  at  least  equal  to  the  unit  shear 
of  concrete. 

(4)  No   initial   strains   are   considered   in   either  the   con- 
crete or  the  steel  due  to  change  of  volume  of  the  concrete 
in  setting. 

(5)  The  concrete  takes  up   the   compression,   while   the 
steel  takes  up  the  tension   and  assists  in  the  resistance  to 
shear. 

67 


68  REINFORCED    CONCRETE. 

(6)  The  form  of  stress-strain  curve  of  concrete  in  com- 
pression is,  as  a  rule,  assumed  as  a  straight  line. 

(7)  Columns  are  designed  for  flexure,  if  the  height  ex- 
ceeds 18  times  the  least  diameter. 

(8)  The  ratio  of  the  modulus  of  elasticity  of  steel  to  that 
of  concrete,  which  varies  with  the  quality  and  bulk  of  the 
concrete,  is  generally  assumed  to  be  10. 

Percentage  of  Steel  Reinforcement.— This  varies  accord- 
ing to  construction,  design,  proportion  in  mixtures  and  is 
different  in  girders,  floor  slabs  and  columns,  as  will  appear 
as  each  detail  is  treated.  As  a  rule,  p  is  a  function  of  the 
ratio  between  the  moduli  of  elasticity,  the  ratio  of  the  actual 
stresses  in  the  steel  and  in  the  concrete,  and  of  the  ratio 
between  the  unit  costs  of  steel  and  concrete.  A  writer  in 
Engineering  News,  June  20,  1907,  sums  up,  in  part,  as  fol- 
lows: 

(1)  When  a  beam  is  strictly  limited  as  to  depth  an  over- 
reinforced  beam  is  the  cheapest. 

(2)  When  beams  or  slabs  are  not  limited  in  dimensions 
by  local  conditions,  the  cheapest  construction  is  that  which 
is    reinforced   for   the   full   utilization   of   both    concrete   and 
steel.     These    conditions    are    easily    shown     graphically    in 
curves,   giving  the   most    economical    percentage    under   dif- 
ferent assumptions.     Thus,  for  the  city  of  New  York,  with 

~-  =  12,  fs  =  16,000  and  fc  =  625,  it  is  found  that  the  most 

£<c 

economical  percentage  is  p  =  0.0062  or  0.62  per  cent  reinforce- 
ment.    See  page  107  for  notation. 

Basis   of   Calculations. — While   the    assumptions    made   in 
design   are   subject   to   considerable   variation,   the   following 
paragraphs  contain  figures  which  are  supported  by  good  en- 
gineering practice  and  can  be  relied  upon: 
Dead  Loads. — The   following  figures  are   for  dead   loads: 

Weight  of  cinder  concrete 120  Ibs.  per  cu.  ft. 

Weight  of  stone  concrete 140  Ibs.  per  cu.  ft. 

Weight  of  reinforced  concrete 150  Ibs.  per  cu.  ft. 

Weight  of  steel 489.6  Ibs.  per  cu.  ft. 

Weight  of  wood  or  tile  floors 20  Ibs.  per  sq.  ft 


BUILDING  DESIGN  AND  CONSTRUCTION.          69 

Live  Loads.  —  In  the  absence  of  uniformity  in  American 
practice  regarding  a  general  method  of  assuming  live  loads, 
the  following  is  recommended,  from  the  Prussian  building 
code,  as  being  safe  and  economical: 

Structural  parts  subject  to  moderate  impact,  the  actual 
dead  and  live  loads. 

Parts  subject  to  higher  impact  or  widely  varying  loads, 
the  actual  dead  load  and  \l/2  times  the  live  load. 

Parts  subject  to  heavy  shocks,  the  actual  dead  load  and 
twice  the  live  load. 

Allowable  Stresses.  —  The  allowable  stresses  in  reinforced 
concrete  must  necessarily  depend  upon  many  factors.  The 
following  figures  are  general,  and  are  to  be  supplemented  by 
reference  to  Floors,  Columns,  etc.  They  refer  to  a  mixture 
not  leaner  than  1  to  6. 

Reinforced  concrete  in  tension,  0  Ibs.  per  sq.  in. 

Reinforced  concrete  in  compression,   750   Ibs.   per  sq.   in. 

Reinforced  concrete  in  shear,  75  Ibs.  per  sq.   in. 

Steel  in  tension,  with  factor  of  safety  of  4,  16,000  Ibs.  per 
sq.  in. 

Steel  in  compression,  10,000  Ibs.  per  sq.  in. 

Steel  in  shear,  10,000  Ibs.  per  sq.  in. 

Bending  Moments   for   Beams.*  —  The   negative   moments 
over   the  supports  of  a   continuous  beam  on   both   sides   of 
these  supports  produce  tension  in  the  upper  portion  of  the 
beam. 
Let  ^/g=  bending  moment  at  support  for  center  load. 

M'^=  bending  moment  at  support  for  uniformly  distributed  loads. 
W  =  total  load  upon  each  beam  in  pounds. 

•w  ==  uniformly  distributed  load  in  Ibs.  per  foot  of  beam. 
/     =  length  of  beam  in  feet. 

Wl 
Then  M'^  =  —  -g—  ft.  Ibs.  ; 


•After    Taylor    and    Thompson,    "Concrete,    Plain    and    Rein- 
forced."    Also  see  page    140  for  Ultimate  Strength  of  Beams. 


70  REINFORCED    CONCRETE. 

The  percentage  of  reinforcement  required  by  these  mo- 
ments is  determined  by  the  methods  employed  when  the  steel 
is  in  the  bottom  of  the  beam  and  the  distance  of  the  steel 
from  the  surface  of  concrete  is  the  same  in  the' two  cases.  If 
the  beams  on  both  sides  of  the  support  are  fully  loaded,  the 
bending  moment  for  central  loads  is  usually  considered 

Wl 
to  be  -JT  or  one-half  the  moment  of  a  beam  supported  at  the 

ends,  and  the  moment  for  uniformly  distributed  loading  to  be 

wl* 

~2g  or  one-third  the  moment  of  a  beam  supported  at  the  ends. 

However,  the  maximum  bending  in  either  of  the  beams  will 
occur  when  it  is  under  stress  and  the  beam  next  to  it  is 
not  under  stress.  Mr.  A.  Considere  states  that  French  en- 
gineers assume  the  safe  minimum  of  the  moment  on  the 

wP 
supports  to  be  only  ^   basing  the  resistance  at  the  center  of 

a  beam  uniformly  loaded  upon  a  positive  bending  moment  of 

wP 

10 

At  present,  engineers  in  the  United  States  have  generally 
adopted  this  rule  to  be  on  the  safe  side.  This  will  in  inch 
pounds  be  written: 

r* 

M"=~^-    zvP  inch  Ibs (3) 

D  O 

Bending  Moments  for  Slabs. — While  the  formulas  for 
floor  beams  and  girders  are  well  supported  by  actual  tests, 
the  floor  slabs,  particularly  those  reinforced  in  more  than 
one  direction,  show  frequent  inaccuracies  of  present  theories 
by  exhibiting  a  strength  considerably  greater  than  calculated. 

The  theory  of  flat  plates  is  so  intricate  that  calculations 
are  not  often  attempted  and  comparative  tests  show  that 
the  strength  of  slabs  continuous  in  both  directions  is  several 
times  greater  than  slabs  supported  at  the  two  ends,  so  that 
the  dimensions  and  reinforcements  may  be  deduced  empir- 
ically. Mr.  Joseph  R.  Worcester*  in  testing  floor  slabs  re- 

*  Journal  Assoc.  Engineering  Societies,  April,  1905;  p.  205. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


71 


i  i 


5! 

I! 

Ifc 


•<.••>. 
« 


^ 

rt         o 


-eS 

1  -B 


I      5 


+ 


.il 


72  'REINFORCED   CONCRETE. 

inforced  with  steel  wire,  found  that  the  steel,  if  calculated 
by  the  usual  theories,  attained  in  one  case  an  apparent  ten- 
sion of  250,000  Ibs.  per  sq.  in.  before  rupture,  thus  showing 
the  evident  inaccuracies  of  present  theories  for  continuous  slabs. 

Hennebique*  found  by  tests  of  floor  slabs  at  the  Paris 
Exposition  that  the  bending  moment  at  the  middle  of  a  slab 
continuous  in  both  directions  was  less  than 

s? 

36' 

Meanwhile  the  building  laws  of  New  York  permit  the 
calculation  of  the  bending  moment  of  square  floor  plates,  re- 
inforced in  both  directions  and  supported  on  four  sides  by 
the  formula 

Wl  . 
MB  =  ^it.  Ibs. 

If  the  length  of  the  slab  exceeds  1.5  times  its  width  the 
entire  load  should  be  carried  by  transverse  reinforcement. 

Square  slabs  may  well  be  reinforced  in  both   directions. 

The  following  method  is  recognized  to  be  faulty,  but  it  is 
offered  *s  a  tentative  method  which  will  give  results  on  the 
safe  side.  The  distribution  of  load  is  first  to  be  determined 
by  the  formula 


r_ 

" 


in  which  r  =  proportion  of  load  carried  by  the  transverse 
reinforcement. 

/  =  length  of  slab 

b  =  breadth  of  slab 

For  various  ratios  of  —  the  values  of  r  are  as  follows: 
o 


0.5 

0.59 

0.67 

0.75 

0.80 

0.83 


*Beton   &   Eisen,    1903,    Heft   I. 


BUILDING  DESIGN  AND  CONSTRUCTION.          73 

Using  the  values  above  specified  each  set  of  reinforce. 
ment  is  to  be  calculated  in  the  same  manner  as  slabs  having 
supports  on  two  sides  only,  but  the  total  amount  of  rein- 
forcement thus  determined  may  be  reduced  25  per  cent  by 
gradually  increasing  the  rod-spacing  from  the  third  point  to 
the  edge  of  the  slab. 

Cross  Reinforcement  in  Slabs.  —  The  author  finds  that 
steel  rods  parallel  to  the  principal  supports  greatly  increase 
the  strength  of  the  slab  and  render  expansion  joints  unnec- 
essary. In  fact,  by  using  a  wire  fabric  a  "lateral  continuity" 
is  gained  which  causes  the  author  to  use  these  formulas 
when  building  codes  will  permit: 

wl2, 

M  =—  -it.  Ibs.,      and 
lo 


respectively,  for  slabs  continuous  over  two  supports  and  over 
four  supports,  for  uniformly  distributed  loads,  in  calculating 
the  middle  of  the  slab,  and  tests  have  invariably  proved  that 
the  dimensions  resulting  have  been  ample  and  safe. 

Shearing  Provisions.  —  There  are  two  general  methods  of 
reinforcing  against  diagonal  and  shearing  stresses  which  may 
be  used  singly  or  in  combination.  One  of  these  consists  in 
bending  all,  or  part,  of  the  longitudinal  bars  up  toward  the 
supports  at  various  points.  The  other  method  involves  the 
use  of  stirrups,  either  vertical  or  inclined,  which  should  be 
attached  to  the  main  reinforcement. 

It  is  desirable,  and,  in  fact,  essential,  in  all  beam  work 
that  some  provision  be  made  for  web  stresses;  otherwise,  if 
failure  should  occur,  it  would  be  sudden  and  without  warn- 
ing. When  the  two  systems  of  web  reinforcement  are  used 
in  combination  the  analysis  becomes  uncertain,  and  it  is 
impossible  to  predicate  the  distribution  of  the  stresses.  We 
will,  accordingly,  consider  ihe  two  methods  separately. 


74  REINFORCED    CONCRETE. 

When  bars  are  bent  up  at  intervals  near  the  supports, 
the  inclined  portions  act  as  the  diagonals  of  a  truss,  taking 
tension,  and  the  stress  carried  is  a  function  of  the  inclination. 
Adjacent  diagonals  should  overlap  sufficiently  to  insure 
"truss"  action. 

It  is  necessary  that  the  inclined  bars  have  sufficient 
length  of  imbedment  above  the  neutral  axis  to  develop  the 
requisite  stress.  Since  the  length  of  imbedment  is  necessarily 
limited,  a  bar  with  a  strong  mechanical  bond  is  especially 
useful  for  such  purposes.  In  this  conception  of  the  action 
occurring  in  the  beam,  all  the  bars  are  considered  to  act  as 
a  unit,  owing  to  their  rigid  connection  through  the  concrete, 
the  bent-up  bars  acting  as  attached  diagonals  to  the  main 
member. 

Stirrups  are  generally  used  vertically,  and  we  will  consider 
only  the  case  of  vertical  stirrups  carried  under  the  longi- 
tudinal bars  and  extending  to  the  top  of  the  beam.  Assum- 
ing no  tension  in  the  concrete,  or  that  this  discussion  applies 
only  after  the  concrete  is  itself  unable  to  resist  the  diagonal 
tensile  stresses  developed,  we  may  say  that  the  stress  in 
any  stirrup  is  equal  to  the  variation  in  the  total  stress  in  the 
longitudinal  reinforcement  in  the  distance  tributary  to  that 
stirrup.  It  is  assumed  that  the  stirrups  carry  only  vertical 
stresses,  all  horizontal  stresses  being  transferred  to  the  lon- 
gitudinal bars  through  bond  with  the  concrete.  Vertical 
stirrups  should  be  investigated  for  sufficiency  of  bond  above 
the  neutral  axis  of  the  beam,  and  owing  to  the  short  length 
of  imbedment  available,  it  will  be  desirable  to  use  a  me- 
chanical bond  bar,  if  no  form  of  anchorage  is  provided. 

Location  of  Stirrups  in  Beams.— The  newest  theory  re- 
garding diagonal  cracks  in  beams  attributes  them  to  internal 
tension  caused  by  a  stretching  and  slipping  of  the  rods  em- 
ployed in  the  reinforcement.  Theoretically,  the  stirrups 
should  slope  45°  away  from  the  center  of  the  beam,  although 
for  practical  reasons  they  are  frequently  set  vertically. 


BUILDING  DESIGN  AND  CONSTRUCTION.          75 

Mr.  E.  L.  Ransome's  empirical  rule  for  spacing  stirrups 
is  to  place  the  first  a  distance  from  the  end  of  a  beam  cor- 
responding to  one-quarter  the  depth  of  the  beam,  the  second 
a  distance  of  one-half  the  depth  of  the  beam,  beyond  the 
first,  the  third  a  distance  of  three-quarters  the  depth  of  the 
beam  beyond  the  second,  and  the  fourth  a  distance  of  the 
depth  of  the  beam  beyond  the  third.  Having  found  this  rule 
very  simple,  practical  and  corresponding  with  calculations 
the  author  generally  employs  it. 

Total  area  of  stirrups  at  one  end  of  a  beam  b  inches  wide 
and  /  inches  long  (total  span)  is  in  square  inches: 

a  =  0.00074  bl 
if  stirrups  are  inclined  45°,  and 

a  =  0.00104  bl 
if  stirrups  are  placed  vertically. 

If  one-half  of  the  beam  tension  rods  are  bent  up  at  the 
quarter  point  as  is  usual,  sufficient  stirrup  area  at  each  end 
of  beam  is  found  by  using  the  first  formula. 

These  formulas  are  based  upon  a  total  shear  at  sup- 
port of 

A=  150  Ibs.  per  sq,  in. 
bjd 

and  a  unit  shear  in  concrete  of  not  to  exceed  50  Ibs.  per  sq.  in. 

For  concentrated  loads  the  stirrups  can  be  figured  as  for 
shear,  the  horizontal  shear  s  being  constant  and  approxi- 

n/ 
mately  equal  to  the  vertical  shear  —  divided  by  the  depth  d. 


76 


REINFORCED   CONCRETE. 


In  locating  stirrups  as  in  a  plate  girder*  the  simplest 
method  is  to  draw  the  shear  diagrams  for  concentrated  and 
distributed  loads.  To  determine  the  spacing,  an  area  equal 
to  the  adhesion  is  subtracted  from  the  shear  diagram  and 
the  remaining  area  is  divided  into  panels,  giving  each  an  area 
to  correspond  with  the  maximum  shear  allowed  for  each 
stirrup.  As  the  height  of  the  panels  decreases,  their  length 
increases,  giving  a  series  of  spaces  representing  graphically 
the  spacing  of  the  stirrup.  Thus  Fig.  31  represents  the  shear 
diagram  of  a  beam  with  a  uniform  and  a  concentrated  load- 
ing. The  area  above  the  line  A  B  represents  the  shear  due 
to  the  concentrated  load  P,  and  that  below  the  line  A  B  the 
shear  due  to  the  uniformly  distributed  load — only  consider- 
ing the  portion  of  the  shear  diagram  to  the  right  of  the  cen- 


Fig.    31.— Diagram   for   Locating   Stirrups. 

ter  line  of  the  beam.  Then  if  the  area  above  the  dotted  line 
kl  represents  the  allowable  stress  cared  for  by  the  adhesion 
of  the  rods,  the  portion  of  stress  in  the  diagram  below  this 
line  must  be  provided  for  by  stirrups.  If  this  be  divided 
in  equal  areas,  a,  one  for  each  stirrup,  the  horizontal  dimen- 
sions of  the  trapezoids,  a,  will  give  graphically  the  desired 
stirrup  spacing.  Also  see  Shear,  p.  227. 

Adhesion  of  Concrete  to  Steel. — The  adhesion  of  concrete 
to  steel  depends  upon  the  richness  of  the  concrete  and  has 
been  found  to  reach  700  Ibs.  per  sq.  in.  Where  the  yield 
point  of  the  steel  is  not  exceeded,  the  minimum  ultimate  ad- 
hesion for  first-class  concrete  may  be  placed  at  275  Ibs.  per 
sq.  in.,  according  to  Mr.  Paul  Christophe,  and  for  a  shear- 
ing strength  of  concrete  equal  to  400  Ibs.  per  sq.  in.  this  cor- 

*Reid,  Concrete  and  Reinforced  Concrete  Construction,  p.  311, 


BUILDING  DESIGN  AND  CONSTRUCTION.          77 

responds  to  a  minimum  clear  distance  between  rods  of  about 
\l/4  times  the  diameters  of  rods. 

Modulus  of  Elasticity. — The  modulus  of  elasticity — or  "the 
ratio  between  stress  and  strain" — of  steel  varies  from 
28,000,000  to  31,000,000  Ibs.  per  sq.  in.,  and  30,000,000  Ibs. 
is  usually  taken  as  an  average  value.  The  modulus  of  elas- 
ticity of  concrete  varies  considerably,  from  1,500,000  Ibs.  per 
sq.  in.  to  5,000,000  Ibs. 

The  following  tabulation  gives  an  idea  of  the  variation  as 
compared  with  different  proportions: 


Broken  stone  or 
gravel  concrete 

Proportions 

Modulus  of  Blast. 
Ibs.  per  sq.  in. 

1—  li—  3 
1—2  —4 
1—2*—  5 
1—3—6 
1—4  —8 

4,000,000 
3,000,000 
2,500,000 
2,000,000 
1.500,000 

Cinder  concrete         1—  2—5  850,000 

However,  for  graded  mixtures  considerably  higher  values 
may  be  found. 

The  higher  the  modulus  of  elasticity  of  the  concrete  the 
lower  should  be  the  percentage  of  steel  and  the  greater  the 
depth  of  the  beam  for  symmetrical  design,  maintaining  fixed 
relations  of  pull  in  steel  to  pressure  of  concrete. 

Summary  of  Talbot's  Tests  on  Tee  Beams.— From  the 
summary  of  the  discussion*  referring  to  the  theory  of  re- 
inforced concrete  tee  beams,  the  following  is  of  particular  in- 
terest to  the  designer: 

(1)  Beams  of  flange  width  of  2,  3  and  4  times  the  width 
of  stem  or  web  and  reinforced  in  each  case  with  steel  equal 
to  1  per  cent  of  the  inclosing  rectangle  (an  imaginary  rectan- 
gle as  wide  as  the  flange  and  as  deep  as  the  distance  from 
the  centroid  of  longitudinal  metal  reinforcement  to  most 
strained  fiber  in  compression)  exhibited  in  a  common  way 
the  characteristics  of  rectangular  beams,  and  the  critical 
failure  in  every  case  came  through  the  longitudinal  reinforce- 
ment becoming  stressed  beyond  its  yield  point. 

*Prof.  A.  N.  Talbot,  Bulletin  Univ.  of  111.,  Feb.  1,  1907. 


78  REINFORCED    CONCRETE. 

(2)  The  full  compressive  strength  of  the  concrete  at  the 
most  remote  fiber  was  not  developed  at  the  yield  point  of 
the   beam,  even   in   the   beams   which   were   reinforced  with 
steel  of  54,000  Ibs.  pr  sqare  inch  yield  point. 

(3)  The  vertical  stirrups  used  proved  to  be  very  effective 
web   reinforcement.     The   diagonal   tension   cracks   appeared 
at  or  above  loads  at  which  failure  by  diagonal  tension  may 
be  expected  in  beams  without  web  reinforcement.     A  high 
resistance    to    diagonal    tensile    stresses    was    developed,    as 
measured  by  the  calculated  maximum  vertical  shearing  unit 
stress,  which  in  one  beam   was  605  Ibs.   per  sq.   in.      Since 
no  beam  failed  by  diagonal  tension,  the  limit  of  strength  of 
the  web  reinforcement  was  not  determined. 

(4)  The  maximum  strength  of  tee  beams  to  resist  hori- 
zontal tension   and  compression    (flange   stresses)    may  well 
be  calculated  by  using  the   ordinary  methods  and   formulas 
in  use  for  rectangular  beams  and  considering  the  inclosing 
rectangle  of  the  tee  beam  to.  be  the  equivalent  rectangular 
beam.     This   approximation    is   at   least   applicable    for    rein- 
forcement not  exceeding  1  per  cent  of  the  inclosing  rectan- 
gle.    The  effective  width  of  a  Tee  beam  should  not  exceed  Y\ 
of   span   length   of   beam  and   its   overhanging   width   on   either 
side  of  the  web  should  not  exceed  4  times  the  thickness  of  the 
slab. 

FOUNDATIONS. 

Types  of  Foundations. — The  type  of  foundation  for  a 
building  depends  upon  the  weight  of  the  proposed  building 
and  the  character  of  the  underlying  soil.  When  the  weight 
of  the  building  has  been  estimated,  the  character  of  the  soil 
will  determine  the  form  of  foundation.  Careful  borings 
should  be  taken  showing  location  of  hard  pan  or  the  condi- 
tion of  the  different  strata,  their  thickness  and  water-bearing 
qualities,  which  will  determine  whether  piling,  caissons,  floats 
or  rafts  be  required.  The  location  and  condition  of  adja- 
cent buildings  must  be  considered,  as  their  maintenance  gen- 
erally devolves  upon  the  contractor  for  the  new  structure. 


BUILDING  DESIGN  AND  CONSTRUCTION.  79 

As,  however,  these  conditions  and  the  selection  of  the 
foundations  required  must  be  met  at  any  event,  we  shall 
only  describe  the  most  usual  methods  used  in  connection 
with  reinforced  concrete  structures. 

Reinforced  concrete  foundations  may  be  classified  as  pile, 
slab,  raft,  mat,  and  portable  foundations. 

Bearing  Power  of  Soils. — The  following  tabulations, 
which  are  self-explanatory,  are  useful  in  connection  with  the 
designing  of  foundations;  they  show  the  bearing  power  of 
soils  in  tons  per  square  foot: 

(From  Baker's  Masonry  Construction.) 

Rock,  the  hardest,  thick  layers,  in  native  bed 200  tons 

Rock,  equal  to  the  best  ashlar  masonry 25  to  30  tons 

Rock,   equal  to  the  best  brick  masonry 15  to  20  tons 

Rock,  equal  to  poor  brick  masonry 5  to  10  tons 

Clay  on  thick  beds,   always   dry 4  to  6  tons 

Clay  on   thick  beds,   moderately  dry    2  to  4  tons 

Clay,    soft    1  to  2  tons 

Gravel  and  coarse  sand,  well  cemented 8  to  10  tons 

Sand,    compact   and   well   cemented 4  to  6  tons 

Sand,   clean  and  dry 2  to  4  tons 

Quicksand,  alluvial  soils,   etc 0.5  to  1  ton 

(From  Building  Code,  National  Board  of  Fire  Underwriters.) 

Soft  clay    1  ton    per  sq.  ft. 

Clay  and  sand  together,  wet  and  springy 2  tons  per  sq.  ft. 

Loam,  clay,  or  fine  sand,  firm  and  dry 3  tons  per  sq.  ft. 

Very  firm  coarse  sand,  stiff  gravel  or  hard  clay.. 4  tons  per  sq.  ft 

Pile  Foundations. — Concrete  piling  offers  many  advan- 
tages which  are  not  obtained  with  timber  piling.  Concrete 
piles  of  the  same  strength  and  bearing  capacity  need  not  be 
so  long  as  those  of  wood,  and  they  need  not  be  so  numer- 
ous. Timber  piles,  to  prevent  decay,  must  be  cut  off  at  mean 
low  water,  and  the  footings  must  be  started  from  this  point. 
With  concrete  piling,  the  tops  can  be  left  just  far  enough 
below  the  bottoms  of  the  columns  to  allow  for  a  footing 
thick  enough  to  carry  the  superimposed  building. 

Concrete  piles  are  of  two  classes:  (1)  Piles  molded  in 
place,  and  (2)  piles  molded  on  the  surface  and  driven  after 
having  become  hard,  as  a  timber  pile  is  driven.  The  Ray- 
mond and  Simplex  piles,  described  here,  belong  to  the  first 
class  and  the  Corrugated  and  Chenoweth  piles  belong  to  the 
second  class. 


80 


REINFORCED    CONCRETE. 


The  Raymond  Pile. — This  pile,  controlled  by  the  Ray- 
mond Concrete  Pile  Co.,  Chicago,  is  placed  in  the  ground 
by  the  pile  core  method,  which  is  as  follows:  A  collapsible 
steel  core,  encased  in  a  thin,  closely  fitting  sheet  steel  shell, 
is  driven  by  a  pile  driver  to  the  required  depth. 


Fig.  32. — Raymond  Collapsible  Steel  Core. 

Fig.  32  shows  two  views  of  this  core,  the  view  to  the  left 
showing  the  shell  driver  and  the  core  expanded.  The  view  to  the 
right  shows  the  pile  core  collapsed  and  ready  to  be  drawn  from 


BUILDING  DESIGN  AND  CONSTRUCTION.          81 

the  shell.  This  shell,  which  is  left  in  the  ground,  acts  as  a 
mold  for  the  concrete,  protecting  it  from  back  pressure,  which 
would  distort  the  pile,  and  from  the  admixture  of  foreign  mat- 
ter, which  would  impair  the  bond  of  the  concrete.  An  electric 
light  can  be  lowered  at  intervals  during  the  placing  of  the  concrete, 
to  enable  the  operator  to  see  just  what  condition  prevails.  When 
reinforcement  is  desired,  the  reinforcing  material  is  inserted 
in  the  shell  before  the  placing  of  the  concrete.  The  piles  are 
tapered  to  obtain  greater  bearing  value,  since  the  load  on  a 
tapered  pile  is  more  uniformly  distributed  along  the  entire 
length. 

Fig.  32-A  shows  a  comparison  between  wooden  piles  and 
concrete  piles,  where  22  wooden  piles  and  an  8-ft.  deep  solid 
concrete  pier  were  replaced  by  8  concrete  piles  and  two 
piers  5  ft.  deep  connected  by  an  arch  construction, 

An  excellent  example  of  the  economy  of  concrete  piles  is 
given  in  the  following  extract  of  a  report  by  Mr.  Walter  R. 
Harper,  showing  a  comparison  in  cost  of  foundation  with 
wooden  piles  and  with  Raymond  piles  in  the  Academic  building 
at  Annapolis : 

The  difference  in  thickness  of  concrete  footings  is  well  illus- 
trated by  a  section  of  the  footings  of  the  academic  building 
with  wood  piles  and  the  same  section  as  redesigned  and  built 
with  concrete  piles.  This  saving  in  excavation  and  footings 
depends  upon  the  height  of  the  building  above  mean  low  water. 
At  the  Naval  Academy  the  rise  and  fall  of  the  tide  in  the 
Severn  river  is  very  slight,  consequently  the  buildings  have  been 
placed  only  a  few  feet  above  mean  low  water.  Notwithstand- 
ing that  the  cost  per  linear  foot  for  concrete  piles  far  exceeds 
that  of  wood  piles,  being  about  four  times  as  much,  the  saving 
in  the  entire  foundation  by  their  use  will  surprise  the  uninitiated, 
as  will  be  seen  by  a  glance  at  the  cuts  shown  here. 

In  the  diagram,  Fig.  32-B,  the  section  E-F  shows  the 
footing  of  the  connection  between  the  library  and  academic 
building  as  designed  by  Mr.  Flagg  for  wood  piles.  Another 
sketch  shows  the  same  section,  G-H  in  the  diagram  as  built  with 
concrete  piles.  The  depth  of  footing  on  this  section  was  re- 


82 


REINFORCED    CONCRETE. 
I 


BUILDING  DESIGN  AND  CONSTRUCTION. 


83 


duced  from  7  ft.  to  2  ft.  8  ins.,  and  the  width  on  the  bottom 
from  12  ft.  1  in.  to  5  ft.  2  ins.  The  area  of  the  cross-section 
was  reduced  from  58  to  12  sq.  ft.  In  the  plan  of  the  wood 
piles  under  the  library  tower  there  are  202  piles  in  a  rectangle 
38  ft.  5%  ins,  square.  The  plan  of  the  same  tower  foundation 
with  84  concrete  piles  has  footings  8  ft.  2  ins.  wide. 


'  <  Tfmbtr  Piles, 


With  wood  piles  it  will  be  noticed  that  the  piles  and  foot- 
ings extend  over  the  entire  rectangle,  while  with  concrete  piles 
the  piles  and  footings  are  only  8  ft.  2  ins.  wide  and  directly 
under  the  walls  of  the  tower.  The  depth  of  the  footing  was 
reduced  by  the  use  of  concrete  piles  from  10  ft.  1%  ins.  to  4 
ft.  1%  ins.  Twenty-seven  12-ins.  31^-lb.  I-beams  were  done 
away  with. 

The  following  reductions  on  the  foundations  of  the  two 
buildings  were  by  the  use  of  concrete  piles:  2,193  wood  piles 
were  replaced  by  885  concrete  piles ;  4,542  yds.  of  .excavation 
were  reduced  to  1,038  yds.,  saving  3,504  yds.,  and  3,250  yds.  of 
concrete  footings  were  reduced  to  986  yds.,  saving  2,264  yds. 

With  wood  piles,  after  excavating  to  mean  low  water,  shor- 
ing and  pumping  would  have  been  necessary  in  all  trenches, 
and  this  saving  was  estimated  at  $4,000.  A  schedule  of  changes 
showing  the  saving  by  the  use  of  concrete  piles  is  given  in  the 
accompanying  tabulation . 

The  saving  in  the  cost  of  foundations  by  the  use  of  concrete 
piles  was  $27,458.18,  or  more  than  half  of  the  original  cost  of 
the  foundations,  as  designed  with  wood  piles. 


84  REINFORCED   CONCRETE. 

COMPARATIVE  COST  OF  WOOD  AND  CONCRETE  PILES. 

Wood  Piles. 

2,193  piles    at  $9.50     $20,835.50 

4,542    cu.   yds.   excavation at       .40         1,816.80 

3,250  cu.  yds.   concrete at     8.00       26,000.00 

5,222  Ibs.   I-beams at       .04  208.88 

Shoring   and    pumping 4,000.00 

Total    cost    $52,861.18 

Concrete   Piles. 

855  piles    at  $20.00     $17,100.00 

1,038  cu.  yds.  excavation at        .40  415.00 

986    cu.    yds.    concrete at       8.00         7,888.00 

Shoring   and   pumping 

Total   cost    $25,403.00 

Difference   in  cost   $27,458.18 

The  estimate  of  length  of  wood  piles  was  taken  from  the 
length  of  wood  piles  driven  in  the  marine  engineering  build- 
ing, a  structure  about  200  ft.  from  the  library  site.  Wood 
piles  would  have  been  required  40  ft.  in  length  at  a  cost  of  20 
cts.  a  foot,  and  would  have  been  on  an  average  driven  30  ft. 
below  mean  low  water,  which  at  5  cts.  a  foot  would  mean  an 
average  cost  of  $9.50  per  pile. 

For  the  estimate  of  excavations  it  was  assumed  that  the  en- 
tire site  was  at  an  elevation  of  7  ft.  above  mean  low  water, 
which  is  an  average  of  the  existing  conditions. 

The  longest  concrete  pile  driven  was  29.7  ft.,  but  owing  to 
the  solid  nature  of  the  soil  at  the  southerly  end  of  the  library 
building,  where  shorter  piles  were  used,  the  average  length  was 
1C  ft.,  and  the  cost  of  the  concrete  piles  was  taken  at  $20  per 
pile. 

The  concrete  pile  selected  was  that  of  the  Raymond  Con- 
crete Pile  Co.,  of  Chicago.  It  is  conical  in  shape,  running  from 
6  ins.  in  diameter  at  the  bottom  to  20  ins.  at  the  top.  Owing 
to  this  conical  shape  the  ground  is  compacted  and  a  mucl: 
shorter  pile  can  be  used  with  this  style  than  with  a  cylindrical 
pile.  The  difference  in  bearing  power  between  a  conical  and 
a  cylindrical  pile  was  shown  by  an  experiment  tried  on  this  work 
at  the  Naval  Academy.  A  Raymond  pile  core  tapered  from  6 
ins.  at  the  point  to  20  ins.  at  the  head,  was  driven  19  ft.  until 
the  penetration  under  two  blows  from  a  2,100-lb.  hammer  fall- 
ing 20  ft.  was  %  in.  A  wood  pile  91/£  ins.  at  the  point  and  11 
ins.  at  the  head  and  having  the  same  length,  19  ft.,  as  the  con- 


BUILDING  DESIGN  AND  CONSTRUCTION.          85 

ical  pile,  had  a  penetration  of  5  5-16  ins.  under  two  blows  of  the 
same  hammer,  falling  20  ft.  This  pile  was  driven  after  the 
concrete  pile  and  about  2  ft.  from  it,  thus  showing  the  com- 
parative bearing  power  between  a  conical  and  a  cylindrical  pile 
of  the  same  length. 

These  piles  of  the  Raymond  style  are  driven  by  the  use  of 
a  hollow  steel  core  6  ins.  in  diameter  at  the  point  and  20  ins. 
at  the  head.  The  cores  used  on  this  work  were  20  and  30  ft. 
in  length.  The  exterior  pieces  of  the  core  are  spread  and  held 
in  place  during  the  driving  by  a  wedge  device.  The  core  is  held 
in  the  leads  of  the  pile  driver  by  steel  plates,  fastened  to  its 
top,  which  form  guides  to  slide  in  the  leads.  The  top  of  the 
steel  core  is  protected  by  a  hardwood  cap  block,  which  sets  in 
a  cavity  made  for  it.  This  block  receives,  the  blow  of  the  ham- 
mer and  has  to  be  renewed  from  time  to  time. 

The  sheet-steel  shells  are  formed  on  the  work  in  an  extra 
heavy  cornice  brake  machine,  and  are  made  in  8-ft.  sections 
with  locked  seams.  The  sections  are  telescoped,  the  point  of  the 
core  is  raised  about  8  ft.  and  inserted  in  the  smallest  section, 
then  the  other  sections  are  drawn  up  around  the  core  by  a  line 
from  the  hoisting  engine  on  the  driver.  Two  drivers  were  used 
on  the  work  at  the  Naval  Academy,  one  with  a  2,240-lb.  drop 
hammer  and  the  other  a  steam  hammer  of  the  Vulcan  make, 
weighing  3,000  Ibs.  The  steam  hammer  was  found  more  sat- 
isfactory, working  much  more  rapidly.  This  was  partly  due 
to  the  fact  that  the  steam  hammer  was  mounted  on  a  turn-table, 
and  was  able  to  turn  in  a  circle  by  its  own  power.  It  was  also 
provided  with  an  extension  top  by  which  the  core  could  be 
raised  or  lowered,  if  necessary,  in  a  trench  below  the  driver. 

The  Simplex  Pile. — The  Simplex  pile,  controlled  by  the  Sim- 
plex Concrete  Piling  Co.,  Philadelphia,  is  constructed  as  follows : 
A  wrought  iron  driving  pipe  of  the  diameter  and  length  of  the 
intended  pile,  and  of  sufficient  strength  to  withstand  driving, 
with  a  point  made  of  cast  iron  or  steel  and  a  hardwood  driving 
head  which  protects  the  pipe  from  injury  during  driving,  is 
driven  to  a  firm  bearing,  and  the  pipe  is  withdrawn  and  the  hole 
filled  with  concrete.  Fig.  33. 


86 


REINFORCED  CONCRETE. 

A 


BUILDING  DESIGN  AND  CONSTRUCTION.          87 

The  Corrugated  Pile.— The  Corrugated  Concrete  Pile  Co. 
of  New  York  manufactures  piles  which  are  polygonal  in 
section  and  are  corrugated  longitudinally  like  a  fluted  col- 
umn. Fig.  34.  There  is  a  hole  extending  the  length  of  the 
pile,  so  that  it  can  be  driven  by  water  jet,  the  water  being 
forced  down  through  the  hole  and  returning  along  the  cor- 
rugated sides. 

The  Pedestal  Pile  is  made  by  MacArthur  Concrete  Pile  & 
Foundation  Co.,  of  New  York,  which  claims  a  large  carrying 
capacity  for  this  pile  on  account  of  the  fact,  that,  in  addition 
to  the  fractional  adhesion,  there  is  a  direct  bearing  power 
of  a  broad  base  resting  in  firm  and  compacted  soil. 

The  apparatus  necessary  to  form  the  Pedestal  Pile  con- 
sists of  a  casing  and  a  core.  The  casing  is  a  steel  pipe 
16  ins.  in  diameter  and  ^  in.  thick,  with  outside  reinforcing 
bands  top  and  bottom. 

The  core  is  a  smaller  and  longer  pipe,  with  a  cast  steel 
point  and  an  enlarged  cast  steel  head.  The  core  fits  inside 
the  casing,  its  enlarged  head  engaging  the  top  of  the  casing 
and  its  lower  pointed  end  projecting  some  4  or  5  ft.  below 
the  casing. 

In  the  head  of  the  core  there  is  an  oak  driving  block 

which  receives  the  blows  of  the  hammer.  The  core  is  fitted 

into  the  casing  and  both  are  driven  into  the  ground  to  the 
desired  depth. 

The  core  is  then  pulled  out  and  a  charge  of  concrete  is 
dropped  to  the  bottom  of  the  casing.  The  rammer  is  now 
lowered  into  the  casing  and  driven  down  through  this  con- 
crete, which  thereby  is  driven  into  the  soil  below  forming 
a  bulb  3  ft.  in  diameter. 


88 


REINFORCED   CONCRETE. 


The  casing  is  then  filled  with  concrete  to  the  top  and 
withdrawn. 

The  Chenoweth  Pile. — This  pile,  shown  in  section  by  Fig. 
35,  is  manufactured  by  Mr.  A.  C.  Chenoweth,  Brooklyn, 
N.  Y.,  by  spreading  a  layer  of  concrete  on  wire  mesk  and 
rolling  both  together  by  a  special  machine  into  a  solid  pile 
with  a  gas  pipe  core  or  center. 

Other  Forms  of  Piles. — Various  patented  forms  of  con- 
crete piles  besides  those  mentioned  above  are  on  the  mar- 


'Reinfyrcement 


Fig.   34. — Section  of 
Corrugated  Pile. 


Fig.  35. — Chenoweth  Pile. 


ket.  In  addition  the  builder  is  free  to  mold  square,  round 
or  polygonal  piles  reinforced  by  longitudinal  bars,  hooping, 
etc.,  in  practically  any  way  desired,  and  such  piles  have  been 
used  in  great  numbers. 

Pile  Driving. — Concrete  piles  may  be  driven  by  jetting 
like  timber  piles,  using  exactly  the  same  methods  and  ap- 
paratus. Concrete  piles  may  also  be  driven  by  hammers, 
using  pile  drivers  of  the  ordinary  type,  but  equipped  to 
handle  the  heavier  concrete  pile.  Care  is  required  in  ham- 
mer driving.  The  pile  must  be  maintained  exactly  in  line 
with  the  direction  of  the  hammer  blow,  a  heavy  hammer  and 
a  short  drop  must  be  employed,  and  the  head  of  the  pile 


BUILDING  DESIGN  AND  CONSTRUCTION.          89 

must  be  protected  by  a  special  cap  to  cushion  the  hammer 
blow. 

For  a  full  discussion  of  the  methods  of  molding  and  driv- 
ing concrete  piles  and  for  detailed  costs  of  pile  foundation 
work  the  reader  is  referred  to  "Concrete  Construction — 
Methods  and  Costs,"  by  Gillette  and  Hill. 

Slab  Foundations. — Slab  foundations  are  of  two  kinds, 
self-contained,  rectangular  slabs,  and  rafts,  where  two  or 
more  columns  are  supported  on  one  slab  so  constructed  that 
the  center  of  gravity  of  the  slab  coincides  with  that  of  the 
superimposed  loads  in  a  manner  to  have  the  weight  of  the 
superstructure  practically  a  constant  on  the  underlying  soil. 
Such  foundations  were  designed  by  the  author  for  the  new 
Battle  House,  Mobile,  Ala.,  the  architects  being  Frank  H. 
Andrews  Co.,  Cincinnati,  O.  The  advantages  of  connecting 
all  separate  footings  by  a  reinforced  concrete  grillage  are 
illustrated  under  Example  of  Building,  page  141. 

For  rectangular  slabs,  such  as  column  foundations,  the 
simplest  construction  is  to  run  the  reinforcement  by  diago- 
nals and  squares,  and  after  deducting  the  area  of  the  col- 
umn base,  to  consider  the  remainder  of  the  slab  as  eight 
cantilevers,  four  running  parallel  to  the  sides  and  four  on 
the  diagonals,  assuming  one-eighth  of  the  load  for  each  sec- 
tion, and  calculating  the  reinforcement  for  each  overhang 
as  a  uniformly  loaded  cantilever.  A  close  approximation  is 
found  by  selecting  the  size  of  rods  and  dividing  the  four 
outsides  of  the  base  into  equal  parts,  as  many  as  are  re- 
quired to  meet  the  steel  area  calculated,  and  draw  in  the 
rods  accordingly.  The  diagonal  rods  will  in  this  manner 
come  closer  together  to  compensate  for  their  longer  lever- 
age. The  thickness  of  the  slab  is  calculated  to  meet  the 
compressive  stresses,  the  same  as  in  any  beam,  and  the  hori- 
zontal shear  likewise. 

In  most  cases  the  horizontal  shear  will  be  taken  care  of  by 
the  concrete  except  for  very  heavy  structures.  As  a  rule,  it  is 
advisable  to  step  off  a  column  footing  rather  than  to  batter 
it,  the  steps  conforming  to  the  theoretical  parabola,  as  shown 


90 


REINFORCED    CONCRETE. 


by  Fig.  36,  owing  to  the  saving  in  labor  and  the  convenience 
in  tamping,  and  the  layers  can  be  arranged  to  follow 
one  another  directly.  Another  method  for  piers  is  to  stiffen 
the  slabs  by  brackets  on  top,  as  was  done  in  the  foundations 
at  the  terminal  station,  Atlanta,  Ga. 

Raft  Foundations. — To  show  the  value  of  a  raft  founda- 
tion for  treacherous  soil,  a  brief  description  is  here  given 
of  the  foundation  for  the  Co-operative  Wholesale  Society, 
Ltd.,  at  Newcastle-on-Tyne,  England.  The  building  rises 
above  the  quay-level  on  which  it  abuts,  and  consists  of  base- 

ment,  ground-floor  and  six  upper 

fc-^j floors.    The  frontage  is  92  ft.  and 

the  depth  125  ft.  The  subsoil  was 
of  the  poorest  quality  for  founda- 
tions, consisting  of  18  ft.  of  made 
ground,  principally  clay,  18  ft.  of 
silt  and  quicksand,  10  ft.  of  soft 
clay,  5  ft.  of  hard  clay,  10  ft.  of 
silty  sand  and  finally  gravel.  The 
above  stratification  had  a  decided 
dip  toward  the  river  Tyne.  To 
carry  the  enormous  weight  of  the 
building,  several  plans  for  founda- 
tions were  proposed.  It  was  at 
first  intended  to  construct  the 
building  of  brick  on  a  foundation 
of  cylinders  6  ft.  6  ins.  in  diam- 
eter, sunk  from  20  to  62  ft.  below 
the  ground  level,  carrying  a  sill  of 
concrete  4  ft.  thick  reinforced  with 
rails.  Another  alternative  consid- 
ered was  the  driving  of  piles  to  the  same  depth,  but  the  liability 
of  injuring  the  adjoining  property  proved  this  method  in- 
advisable. Finally,  both  these  projects  were  abandoned  and 
it  was  decided  to  construct  a  raft  of  reinforced  concrete  over 
the  whole  area  of  the  ground.  This  raft,  as  constructed, 
measures  2  ft.  6  ins.  in  its  thickest  part  and  only  7  ins.  in  the 


\\\ 


XXxx 


3 


XXX 


\\ 


Fig.    36. — Plan   and    Section 
of   Column    Footing. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


91 


thinnest  part,  as  shown  by  Fig.  37.  The  entire  site  is  di- 
vided up  into  rectangles  measuring  generally  14  ft.  8  ins. 
by  14  ft.  6  ins.  Each  side  of  these  rectangles  is  a  reinforced 
concrete  beam  6  ft.  6  ins.  deep  by  2  ft.  5  ins.  wide  at  the 
bottom,  the  reinforcement  being  according  to  the  Henne- 
biqtie  system. 

The  steel  reinforcement  along  the  bottom  of  the  mid- 
spans  consists  of  ten  1^2-in.  round  rods.  At  the  end  of  each 
beam  half  of  the  bars  are  carried  up  to  the  upper  surface, 
this  arrangement  being  a  characteristic  feature  of  the  Hen- 
nebique  system.  Light  steel  stirrups  also  extend  from 
around  the  bottom  bars  up  to  the  upper  surface,  in  the  or- 
dinary manner,  thus  tying  the  concrete  together  in  a  ver- 


Fig.     37. — Raft     Foundation     for     Warehouse,     Newcastle-on-Tyne, 

England. 

tical  direction.  The  concrete  floor  filling  in  each  rectangle 
is  constructed  on  practically  the  same  system;  but  the  bars 
used  are  of  much  lighter  section,  being  in  some  cases  J^-in. 
and  in  others  24-in.  in  diameter.  The  columns  which  sup- 
port the  upper  floors  are  also  of  reinforced  concrete.  .They 
are  placed  at  the  corners  of  the  foundation  "squares."  The 
reinforcement  here  is  of  2-in.  bars,  which  are  carried  right 
into  the  foundation.  At  higher  levels,  where  the  total  load 
to  be  carried  is  naturally  less,  the  reinforcement  is,  of  course, 
much  lighter,  the  weight  of  steel  used  and  the  size  of  the 


92  REINFORCED   CONCRETE. 

columns  being  accurately  proportioned  to  the  load  to  be 
carried.  At  the  foundation  level  the  columns  measure  29 
ins.  square,  and  diminish  to  8  ins.  at  the  sixth  floor.  Thus, 
if  settlement  takes  place,  the  entire  building  settles  as  a 
solid  block,  and  therefore  cannot  suffer  any  deterioration 
from  unequal  settlement.  In  the  particular  case  of  this 
warehouse,  there  has  been  a  settlement  of  3l/2  ins.  at  the 
front  and  of  3  ins.  at  the  rear,  which  took  place  between 
the  date  of  construction  of  the  foundations  and  of  the  first 
floor.  Since  then  no  further  settlement  has  taken  place,  nor 
is  any  anticipated. 

Mat  Foundations. — In  this  construction  the  building  may 
be  considered  as  turned  upside  down  and  the  bearing  power 
of  the  soil  be  considered  as  an  evenly  distributed  load  rest- 
ing on  the  columns,  in  a  manner  similar  to  that  used  by  the 
author  for  the  Cement  Storage  Elevator  at  South  Chicago, 
111.,  described  on '  page  382  and  following ;  at  the  Battle 
House  Hotel,  Mobile,  Ala. ;  the  brokers'  office  and  ware- 
house building,  in  Kansas  City,  Mo.;  and  in  the  mushroom 
system  of  Mr.  C.  A.  P.  Turner,  Minneapolis,  illustrated  by 
Fig.  55,  p.  103.  The  mat  should  first  be  laid  down,  preferably 
a  wire  fabric,  near  the  top  of  a  4-or  6-in.  layer  of  concrete, 
and  the  regular  slab  foundation  supported  on  and  connected 
to  it.  This  will  tie  all  foundations  together  in  a  most  effect- 
ive manner,  will  facilitate  damp-proofing  and,  as  a  rule,  prove 
an  economical  construction. 

Portable  Foundations. — Incidental  to  railroad  construc- 
tion, a  number  of  similar  buildings  are  often  erected  along 
the  line,  such  as  small  depots,  water  stations,  tool  sheds, 
corn  cribs,  coal  trestles,  semaphores,  switch  and  signal  struc- 
tures, etc.,  which  require  concrete  foundations  and  where 
cement  and  aggregates  must  be  shipped  in  by  the  railroad 
in  too  small  quantities  for  economy  and  proper  care-taking. 
In  such  cases  portable  foundations  of  reinforced  concrete 
can  be  manufactured  at  a  location  on  the  line  where  sand 
and  gravel  are  plentiful  and  where  there  can  be  a  good  cem- 
ent warehouse.  These  portable  foundations  are  built  of 


BUILDING  DESIGN  AND  CONSTRUCTION. 


93 


one  small  top  plate  and  one  larger  bottom  plate,  connected 
by  diagonal  ribs  into  the  form  of  a  truncated  square  pyramid 
and  provided  with  holes  and  sockets  for  holding  down  bolts. 
The  hole  for  the  pier  is  dug  as  usual,  the  foundation  lowered 
into  position  and  steadied  at  the  proper  level,  then  the 
backfilling  is  washed  in  and  tamped.  Sand,  being  practically 
of  the  same  weight  as  the  concrete,  will  serve  the  same  pur- 
pose, with  the  difference  that  only  a  small  fraction  of  the 
material  has  been  hauled  from  a  distance.  These  plates 
and  ribs  should  be  made  of  a  rich  concrete  about  1-4,  with 
aggregates  of  maximum  density,  and  reinforced  with  two 
layers  of  wire  fabric  in  each  plate  or  rib,  with  all  vertical 
fabric  tied  to  the  horizontal  where  they  join.  Such  structures 
can  be  moved  without  destroying  the  foundation  or  leaving 

TABLE  XXXVII. — FLOOR  LOADS  FOR  BUILDINGS,  IN  POUNDS  PER  SQUARE 

FOOT. 


Bldg. 

Code 

CLASS  OF  BUILDINGS 

Nat'l 
Board 
of  Fire 

New 
York 
1906 

Chicago 
1905 

Phila- 
delphia 
1904 

St. 
Louis 

San 
Fran- 
cisco 

Under- 

1906 

writers 

1905 

Dwellings,  tenements,  apart- 

ments fiats  .          ... 

60 

60 

40 

70 

60 

60 

Hotels,  lodging  houses  

60 

60 

50 

70 

60 

Offices,  all  floors  except  first 
floor 

75 

75 

50 

100 

70 

75 

Offices  first  floor 

150 

15 

150 

150 

Schools  

75 

75 

75 

100 

75 

Stables  and  carriage  houses 

75 

75 

75 

Public  assembly  ...    . 

90 

90 

100 

120 

100 

125 

Stores  ....               .... 

120 

120 

100 

120 

120 

Light  manufacturing  and 

120 

120 

100 

120 

250 

Heavy  storage,  warehouses. 

150 

150 

100 

150 

150 

250 

or 

or 

Factories,  manufacturing, 

more 

more 

150 

150 

100 

150 

150 

250 

or 

or 

or 

or 

more 

more 

more 

more 

94  REINFORCED    CONCRETE. 

them,  and  in  the  author's  opinion  portable  foundations  will 
with  the  increase  of  manufactured  articles  in  reinforced  con- 
crete form  a  very  considerable  item. 

FLOORS. 

Floor  Loads. — The  construction  of  reinforced  concrete 
floors  depends  upon  their  purpose  and  the  live  loads  that 
are  to  be  supported,  whether  quiescent,  moving  or  with  im- 
pact. Different  cities  specify  different  loads  for  the  several 
classes  of  buildings,  as  may  be  seen  from  Table  XXXVII. 

All  specifications  should  contain  a  condition  or  clause, 
stipulating,  that  the  floor  should  be  tested  within  a  period  of 
90  days  or  more,  for  an  actual  load  equal  to  twice  the  speci- 
fied floor  load — without  any  permanent  deflection. 

This  should  be  considered  a  very  liberal  condition  and 
be  insisted  upon. 

Table  XXXVIII  shows  the  weight  per  cubic  foot  of  va- 
rious substances,  which  are  stored  in  warehouses. 

TABLE    XXXVIli.— WEIGHT* OF'  VARIOUS    SUBSTANCES    STORED    IN 
WAREHOUSES. 

Lbs.  per  cu.  ft. 

Wheat    50 

Beans,  peas,   etc 58 

Flour   in   bulk 36 

Preserved  meats 35 

Loose   hay    . 5 

Baled   hay    20 

Loose   straw 5 

Paper   in    layers 80 

Books  in   layers 58 

Clothing  in  layers 43 

Hardwood   in   layers 29 

Coke 23 

Coal    100 

Loose  snow    14 

Tamped  snow    58 

Brick,  Pressed   ,,,.,,,,,,,.,,,.,,,         150 

Brick,    Common     125 

Earth,   Rammed    90-100 

Granite     170 

Granite   Rubble   Masonry    140 

Granite  Masonry,  Well  Dressed 165 

Limestone 160-170 

Limestone  Rubble  Masonry    165 

Marble    170 

Sandstone 145-150 


BUILDING  DESIGN  AND  CONSTRUCTION.  95 

TABLE  XXXVIII— (Continued). 

Lbs.  per  cu.  ft. 

Slate    175 

Water  (1  cu.  ft.  7.48  U.  S.  gals.) 62 Vz 

Gravel     120 

Sand,   Dry    90-105 

Mortar    100 

Rock    Concrete    150 

Cinder   Concrete    90 

Plaster 140 

Cast  Iron   450 

Steel    480 

Paving  Asphaltum   100 

WEIGHT  OF  BRICK  WALLS,  PER  SUPERFICIAL  FOOT. 


9-inch  wall 84  Ibs. 

13-inch  wall.  .          ..121  Ibs. 


22-inch     wall 205   Ibs. 

26-inch     wall.  .  .  .243   Ibs. 


18-inch  wall 168  Ibs. 

A  bar  of  steel  1-inch  square  and  1  foot  long  weighs  3.40  Ibs. 

Factor  of  Safety. — As  a  rule  for  floors,  the  factor  of  safety 
is  taken  as  the  dead  load  plus  four  times  the  live  load,  di- 
vided by  the  actual  total  floor  load. 

Classification. — A  great  number  of  floor  constructions 
have  developed  both  in  Europe  and  in  the  United  States.  In 
general  they  belong  to  the  following  classes: 

(1)  Slab  Floors,  running  from  girder  to  girder. 

(2)  Beam  Floors,  with  short  span  slabs. 

(3)  Beam    and   Tile    Floors    with    tiles   between   beams, 
making  a    flat   ceiling. 

(4)  Arched  Floors,  with  or  without  cinder  rilling. 

(5)  Manufactured   Floors,   not   made   in   situ. 

(6)  Floors  without  Beams  or  Girders. 

Slab  Floors. — This  is  the  simplest  type  of  reinforced  con- 
crete floor,  and  consists  of  a  slab  resting  on  I-beams,  which 
may  or  may  not  be  encased  in  concrete,  and  the  slabs  may 
be  carried  on  either  the  top  or  the  bottom  flange  of  the 
beam,  or  -on  both.  In  the  second  case,  the  space  to  the  top 
of  the  beams  may  be  filled  with  cinder  concrete,  and  in  the 
latter  case,  a  cinder  filling  may  be  employed  or  the  space 
left  as  an  air  space.  The  reinforcement  may  consist  of  wire 
fabric,  expanded  metal,  or  loose  rods  or  wires  inserted 
singly  and  tied.  The  first  two  are  most  used  in  America. 
The  reinforcement  may  be  placed  along  the  lower  part  of 


96 


REINFORCED    CONCRETE. 


the  slab,  may  curve  from  the  bottom  of  the  slab  at  mid- 
spans  to  the  top  over  the  support,  or  two  sets  of  reinforce- 
ment may  be  used,  one  in  the  upper  and  one  in  the  lower 
part  of  the  slab. 

Expanded  metal  floors  are  very  extensively  used  in  the 
United  States,  as  they  are  easy  to  construct  and  are  emi- 
nently satisfactory.  Fig.  39  shows  a  common  type  of  ex- 


Fig.    39.— Expanded   Metal   Floor   Slab. 

panded  metal  floor,  with  one  of  the  beams  left  exposed,  and 
the  other  protected  by  being  encased  in  three  reinforced 
slabs. 

The  Columbian  slab  floor,  illustrated  by  Fig.  40,  is  re- 
inforced with  bars  resembling  a  double  cross  in  section, 
which  are  suspended  from  the  top  flange  of  the  I-beam  either 


Fig.   40. — Columbian  Slab  Floor. 

by  a  hanger,  which  is  shown  by  Fig.  41,  or  are  riveted  to 
the  web  of  the  beam,  as  shown  by  Fig.  40. 

Monier  reinforcement,  Fig.  42,  is  much  used  in  Europe. 
It  consists  of  carrying  rods  in  the  direction  of  the  span  and 
distributing  rods  of  lighter  weight  crossing  same,  often  with 
an  additional  trellis  near  the  top  surface  of  the  slab.  The 


BUILDING  DESIGN  AND  CONSTRUCTION. 


97 


rods  in  each   netting  are  tied  together  at   intervals,  usually 
with  No.  18  annealed  wire. 

The  Cottancin  system  is  similar  to  the  Monier,  bat  the  carry- 
ing and  distributing  rods  are  of  the  same  size  and  are  in- 
terlaced, as  shown  by  Fig.  43. 


Fig.    41.— Hanger  for 
Columbian    Bars. 


Fig.   42.— Monier 
Slab    Floor. 


Fig.   43.— Cottancin 
Reinforcement. 


The  Roebling  slab  floor  is  of  many  types,  a  common 
form  being  that  illustrated  by  Fig.  44.  The  reinforcement 
is  flat  bars,  which  are  bent  at  the  beams  so  as  to  connect 
with  the  flange,  as  shown.  Spacers  supply  the  place  of  dis- 


BS 


"-Z  *    Flat  Bar  \'.t 

in  Conerete\ 


^ZxIShiptr 


Part      Longitudinal      Section. 


F/crf/ror?    '• 


PaH-     Plan. 
Fig.    44.— Roebling    Flat    Slab    Floor. 

tributing  rods,  and  are  fitted  into  slots  in  the  bars.      Spans 
may  be  constructed  up  to  16  ft. 

The    Matrai    system,   Fig.   45,    has   wires     suspended    from 
fixed    points    and    allowed    to    assume    the    form    of    catenary 


98 


REINFORCED    CONCRETE. 


curves,  the  wires  crossing  diagonally  as  well  as  in  series  par- 
allel to  both  sides  of  the  frame  work. 


X 

si 


Fig.   45.— Matrai  Floor. 

In  either  of  the  above  fabric  systems,   additional  carry- 
ing rods  and  distributing  rods  are  usually  laid  in   to  make 


BUILDING  DESIGN  AND  CONSTRUCTION. 


99 


up  for  such  steel  areas  as  may  be  required  over  and  above 
the  section  furnished  by  the  manufactured  article. 

Beam  Floors. — Beam  floors  are  those  in  which  the  beams 
as  well  as  the  slabs  are  of  reinforced  concrete  and  are  built 
in  one  piece  with  the  slab.  Constructions  vary,  but  gener- 
ally the  floor  system  consists  of  main  girders  carried  by 
columns,  intermediate  beams  or  joists  carried  by  the  main 
girders  and  the  covering  floor  slab  in  one  piece  with  both 
beams  and  girders.  Figure  46  shows  a  fairly  typical  beam 
floor. 


Fig.    46. — Hennebique  Floor  with  Single   Reinforcement. 

The  slab  reinforcement  may  be  of  any  of  the  forms  de- 
scribed in  the  preceding  section,  and  the  girder  reinforce- 
ment may  be  either  loose  rods  or  framed  units.  Several 
forms  of  unit  frames  for  girder  reinforcement  are  described 
in  Chapter  I.  When  loose  rods  are  used  the  arrangement 
consists  of  straight  and  bent  rods  in  some  form  of  alterna- 
tion with,  in  many  types  of  construction,  vertical  or  inclined 
stirrups  anchoring  the  straight  rods  up  into  the  concrete 
above. 


100 


REINFORCED    CONCRETE. 


Examples  of  beam  floors  showing  variations  without  end 
are  available,  but  only  two  are  given  here.  Fig.  46  shows 
a  beam  floor  of  Hennebique  construction,  much  used  in 
Europe.  Fig.  47  shows  a  Ransome  floor  reinforced  with 
twisted  square  rods.  The  drawing  shows  a  section  of  the 
floor  built  in  the  addition  to  the  Pacific  Coast  Borax  Fac- 
tory, Bayonne,  N.  J.  The  designed  load  is  100  Ibs.  dead 


zb"-> 


—  *-J  ____ 


$•*-*—  X~~  '----M- 
?$"*        z°u~Bars,a       c 


K-fi?"*  faW 

U^-L--J---!--! 


V  Rods,!?  Centers 


8,-%  Vertical  Rods 


Intermediate  Girder 


Typical  Transverse 
,„    Floor  Section 


•net 'Walls 


,,„ 
jU-Bar 


Section  C-C. 


Fig.   47.  —  Ransome  Floor,   Pacific   Coast  Borax   Factory. 

load  and  400  Ibs.  uniformly  distributed  live  load  per  square 
foot.  It  will  be  seen  that  two  girders  are  used  at  the  col- 
umns. These  are  separated  by  a  plane  of  cleavage  to  allow 
for  expansion. 

Beam  and  Tile  Floors.  —  In  beam  and  tile  floors  the  tiles 
act    primarily    as    forms    or    scaffold    and    are    placed    from 


on 


"•'*• •&.*??' 


Fig.    48. — Beam    and    Tile    Floor  with    Kahn    Bars. 

3  to  5  ins.  apart,  the  reinforced  concrete  beams  occupying 
the  space  between  the  tiles,  a  2  to  4-in.  slab  being  laid  on 
top  connecting  the  beams  laterally.  The  reinforcement  of 
the  beams  between  the  tiles  may  be  any  that  is  employed  for 
beam  floors.  Such  a  floor  is  light  in  weight,  the  air  spaces 
serving  to  deaden  sound.  Fig.  48  shows  this  type  of  floor 


BUILDING  DESIGN  4ND  CONSTRUCTION 


101 


using  the  Kahn  bar  as  reinforcement,  and  Fig.  49  shows  a 
combination  type  employed  by  the  National  Fireproofing  Co. 
of  Chicago. 

Arch  Floors. — In  arched  floors 
the  different  fabrics  are  em- 
ployed as  for  slab  floors  and 
are  usually  laid  between  struc- 
tural steel  girders  or  beams.  A 
flat  ceiling  is  obtained  by  sus- 
pending metal  lathing  from 
beam  to  beam  and  plastering. 

A  Roebling  arch  floor,  with 
both  flat  and  curved  ceilings,  is 
shown  by  Fig.  50. 


a\ 
X> 
II 


Fig.  49— Beam  and  Tile  Floor, 
National  Fireproofing  Co. 


The  Wuensch  arch  floor,  Fig.  51,  is  reinforced  with  angle 
or  tee-iron  riveted  to  the  I-beams.  This  gives  a  very  strong 
floor. 


Oak  Flooring^     y Spruce  Flooring 


.•5*4  Steepens,  l?"C,ti?C. 


Fig.  50.— Roebling  Arch  Floor. 

The  Monier  arch  Ho  or  is  reinforced  with  Mor.ier  netting, 
either  one  or  two  sets  of  netting  being  employed.  A  very 
heavy  floor  is  obtained  by  placing  the  upper  netting  in  an 


Fig.  51. — Wuensch  Arch  Floor. 

arch,  and  filling  to  a  flat  top   with   lean   concrete.     Fig.  52 
shows  both  the  single  and  the  double  arch  construction. 


102 


REINFORCED    CONCRETE. 


Manufactured  Floors. — Among  manufactured  floors  a 
great  number  of  varieties  have  appeared  abroad  and  are 
gradually  gaming  ground  in  the  United  States. 

The  Siegiwri  system,  Fig.  53,  consists  of  a  hollow  beam 
reinforced  by  round  rods,  its  top  face  forming  the  floor  slab, 
and  its  bottom  face  the  ceiling.  The  sections  are  10  ins. 
wide  with  corrugated  sides  and  the  spaces  are  filled  with 


Fig-.    52. — Single   and   Double   Arch   Monier  Floor. 

mortar.     These  floors  cost  from  15  to  20  cts.  per  square  foot, 
according  to  span  and  load. 

The  Visintini  system,  Fig.  54,  is  also  used  in  the  con- 
struction of  floors  and  roofs  and  consists  of  shallow  beams 
molded  in  advance.  Floors  are  made  up  of  a  series  of  these 
beams  placed  side  by  side,  usually  6  to  12  ins.  wide  and  6 


Fig.  53. — Siegwart  Hollow  Beam.          Fig-.    54. — Visintini   Beams. 

to  8  ins.  in  depth.  In  appearance  they  are  Warren  trusses 
with  no  reinforcement  for  the  web  members  which  are 
stressed  in  compression.  For  deep  trusses  spanning  from 
column  to  column  and  supporting  the  floor  slabs  usually 
Pratt  trusses  are  used,  where  the  verticals  are  in  compres- 
sion and  not  reinforced. 

The   fact   that   a    manufactured   floor    can    be    dismantled 
without  complete  destruction,  and  besides  can  be  manufac- 


BUILDING  DESIGN  AND  CONSTRUCTION. 


103 


tured  under  roof  at  any  time  and  erected  rapidly  with  a  great 
saving  in  scaffolding  and  labor,  will  doubtless  before  long 
bring  this  construction  prominently  before  owners  and  con- 
tractors. 

Floors  Without  Beams  or  Girders. — Floors  without  beams 
or  girders  are  illustrated  by  the  "mushroom"  system,  which 


Fig.    55. — Floor    Slab    Reinforcement,    Mushroom    System. 

is  an  adaptation  of  the  Matrai  system,  excluding  beams  or 
girders,  the  reinforcing  elbow  rod  of  the  head  of  the  col- 
umns being  curved  out  to  receive  a  large  floor  area  directly. 
This  system  is  patented  by  Mr.  C.  A.  P.  Turner,  Minneapo- 
lis, Minn.  The  columns  are  octagonal  or  cylindrical,  and  the 
floor  panels  are  built  up  to  24x24  ft.,  or  26x26  ft.  The  floor 


104  REINFORCED    CONCRETE. 

loads  sustained  are  from  200  to  1,000  Ibs.  per  sq.  ft.     Fig.  55 
shows  the  floor  and  column  reinforcement. 


Fig.  55-A. — Head  Reinforcement  and  Plan  of  Basket. 

The  Umbrella  Flat-Slab  System  is  a  style  of  reinforcement 
for  concrete  columns  and  building  floors  recently  devised  by 
Mr.  W.  P.  Cowles,  of  Minneapolis,  Minn.  As  indicated  in 
the  accompanying  drawing,  it  consists  essentially  of  a  con- 
ical-shaped column  cap,  enclosing  a  system  of  reinforce- 
ment which  extends' partly  into  the  floor  slab.  The  latter  is 
without  beams  or  girders  and  is  reinforced  with  rods  running 
from  each  column  to  each  of  the  eight  on  the  sides  of  the 
square  of  which  it  forms  the  center. 

The  columns  are  continuous  and  have  a  telescope  splice 
in  the  umbrella  head,  which  has  triple-hooping  reinforce- 
ment, insuring,  it  is  claimed,  that  the  load  from  the  column 
above  is  transmitted  to  the  center  of  the  column  below,  thus 
preventing  eccentric  loading.  In  addition  to  the  tension  or 
slab  rods,  cantilever  compression  rods  are  provided  and  are 
distributed  so  as  to  strengthen  the  concrete  in  compression 


BUILDING  DESIGN  AND  CONSTRUCTION. 


105 


at  the  perimeter  of  the  umbrella  head.  Incidentally  they 
tend  to  reinforce  the  slab  at  this  point  in  shear,  and  to  re- 
strain the  concrete  at  the  bottom  of  that  portion  of  the  slab 
forming  the  top  of  the  umbrella  head.  They  lie  directly  be- 
neath the  tension  or  slab  rods. 

The  umbrella  basket  is  designed  to  reinforce  the  head  in 
shear  and  also  to  restrain  the  concrete  forming  the  column 
cap.  This  basket  can  be  assembled  and  spirally  wound  at 
the  shop  by  machine. 


Fig.   55-B. 


Fig.  55-C. — Elevation  of  Column  and  Plan  of  Slab  Reinforcement. 


106  REINFORCED    CONCRETE. 

The  Heidenreich  Flat-Slab  System  employs  metal  fabric 
exclusively  instead  of  loose  rods,  the  compression  and  shear 
above  the  supports  being  met  with  double  reinforcing,  the 
compression  reinforcement  at  the  underside  of  the  slab 
above  supports  being  tied  to  the  tension  reinforcement  in 
the  top  of  the  slab. 

These  reinforcing  bands  of  fabric  run  rectangularly  and 
diagonally  over  the  columns  and  in  one  length  from  end 
to  end  or  side  to  side  of  the  building,  thus  obviating  splices, 
and  the  use  of  fabric  insures  a  greater  lateral  continuity 
than  does  the  use  of  loose  rods,  and  also  greater  safety  in 
the  correct  placing  of  the  steel. 


When  we  add,  that  the  combined  thickness  of  the  four 
unspliced  bands  above  the  columns,  is  approximately  one- 
eighth  of  the  jcombined  thickness  of  the  spliced  loose  rods, 
the  added  value  of  /  d  more  than  makes  up  for  the  higher  pound 
cost  of  the  fabric  reinforcement. 

Calculation  of  Slabs. — The  tables  for  calculation  of  floors 
and  beams  closely  conform  to  the  theory  developed  by  Prof. 
A.  N.  Talbot*,  and  have  been  adapted  to  such  ratio  of 
moduli  of  elasticity  and  permissible  stresses  as  have  been 
adopted  by  New  York  building  regulations.  Other  tables 
show  results  for  richer  concrete  and  other  unit  stresses,  also 
other  ratio  of  moduli  permissible  under  such  conditions. 
The  table  based  upon  the  parabolic  stress-line  deformation 
is  given  for  comparison. f 


"Test  of  Reinforced  Concrete  Tee  Beams,  Univ.  of  111.  Bul- 
letin, Feb.  1,  1907. 

tSee  also  Taylor  &  Thompson,  "Concrete,  Plain  and  Re- 
inforced." 


BUILDING  DESIGN  AND  CONSTRUCTION.         107 
Notation: — 
b  =  breadth  of  flange  or  tee-beam  in  inches 

d  =  distance  from  the  compressive  face  to  the  center  of 
the  metal  reinforcement 

h  =  thickness  of  beam  or  slab 

p  =  ratio   of  area   of  metal   reinforcement   to  area  of  in- 
closing rectangle  above  center  of  reinforcement 

.£"3  =  modulus  of  elasticity  of  the  steel 

EC.  —  initial  modulus  of  elasticity  of  concrete  in  compres- 
sion 

n  =  jr"**  ratio  of  moduli  of  elasticity  of  steel  and  con- 
crete 

fs  =  tensile  stress  per  sq.  in.  in  metal  reinforcement 

fc  —  compressive  stress  per  sq.  in.  in  compression  face  of 
concrete  at  most  remote  fiber 

v—  horizontal  shearing  stress  per  sq.  in.  in  concrete 

fc=  ratio  of  distanced  between  compressive  face  and  neu- 
tral axis  to  distance  d 

Mc  =  resisting  moment  of  concrete 

M»  —  resisting  moment  of  metal  reinforcement 

A"c,  A"s  and  A"v  are  constants,  varying  in  direct  proportion 
with y^.,  fs,  and  v 


138 


REW FORCED   CONCRETE. 


K  =  the  smaller  of  the  two  values  A"c  and  A"s 

V  =  safe  vertical  shear  at  a  given  section  in  Ibs. 

M  -  safe  bending  moment  at  a  given  section  in  inch  Ibs. 

M  =  Kbd? (6) 

F=  KJd (7) 

Kv  =  v(\  —  Y3k} (8) 

Straight   Line   Formula.  —  (See    Fig.    56.)        I.     Rectangular 
Beams. 


Fig.    56. — Rectangular  Line  Diagram. 

k 

7  =  1—3- 

_      M 
fs  ~  pjbd* 

2M 
jkbd* 


P  = 


P  = 


Area  of  steel 
bd 


—  np 


-f) 
(l  —3")  fc 


(9) 


(11) 


BUILDING  DESIGN  AND  CONSTRUCTION. 


109 


Kc  =  fck     l— 


(12) 


(13) 


(14) 


K  =  the  smaller  of  the  two  values  Kc 
and  Ks 

Table  XXXIX  gives  values  of  K  for  various  proportions  of 
steel  used  in  designing  concrete  beams,  slabs,  etc. 

TABLE  XXXIX.  —  VALUES  OF  K  FOR  VARIOUS  PROPORTIONS  OF  STEEL 
USED,  WHEN  ft  =  500;  AND  rt=16,000. 


=  12. 


p 

* 

-1 

Kc 

K, 

K 

k 

'-I 

Kc 

#8 

K 

.001 

.143 

.952 

35.8 

15.2 

15.2 

.158 

.947 

37.6 

15.2 

15.2 

.002 

.196 

.935 

45.8 

29.9 

29.9 

.215 

.928 

50.0 

29.6 

29.6 

.003 

.235 

.922 

54.2 

44.3 

44.3 

.258 

.914 

58.9 

43.8 

43.8 

.004 

.266 

.911 

60.2 

58.4 

58.4 

.291 

.903 

65.8 

57.8 

57.8 

.005 

.291 

.903 

65.8 

72.2 

65.8 

.319 

.894 

71.2 

71.4 

71.2 

.006 

.314 

.896 

70.3 

86.0 

70.3 

.343 

.885 

76.2 

84.8 

76.2 

.007 

.334 

.889 

74.2 

99.5 

74.2 

.366 

.878 

80.3 

98.6 

80.3 

.008 

.352 

.883 

77.7 

113.0 

77.7 

.384 

.872 

83.8 

111.7 

83.8 

.009 

.370 

.877 

81.1 

126.1 

81.1 

.401 

.866 

86.9 

124.7 

86.9 

.010 

.384 

.872 

83.8 

139.8 

83.8 

.417 

.861 

90.0 

137.8 

90.0 

.011 

.398 

.867 

86.4 

152.5 

86.4 

.432 

.856 

92.4 

150.6 

92.4 

.012 

.411 

.863 

88.8 

166. 

88.8 

.444 

.852 

94.8 

163.8 

94.8 

.014 

.435 

.855 

93.0 

192. 

93.0 

.470 

.843 

99.1 

188.5 

99.1 

.016 

.456 

.848 

96.7 

217. 

96.7 

.492 

.836 

103.0 

214.0 

103.0 

.018 

.476 

.841 

100.0 

243. 

100. 

.513 

.829 

106.0 

238.3 

106.0 

.020 

.493 

.836 

103. 

267. 

103. 

.530 

.823 

108.8 

263.2 

108.8 

.030 

.561 

.813 

114. 

390. 

114. 

.600 

.800 

120.0 

384. 

120.0 

.040 

.610 

.796 

122. 

510. 

122. 

.650 

.784 

127.6 

502. 

127.6 

.050 

.650 

.783 

127. 

628. 

127. 

.680 

.774 

131.8 

620. 

128.2 

n=15. 


110 


REINFORCED    CONCRETE. 


When  high  carbon  steel  is  used  as  a  reinforcement  with  a 
rich  concrete,  we  may  assume/s  =  20,000  and/c=750.  Table  XL 
uses  these  values.  The  selection  of  the  vaiue  of  n  depends  upon 
the  bulk  of  the  concrete  as  Ec  assumes  a  higher  value  for  light 
constructions  than  for  heavy  ones. 


TABLE  XL. — VALUES  OF  K  FOR  VARIOUS  PROPORTIONS  OF  STEEL  USED 

WHEN  /c  =  750,    AND  /»  =  20,000. 


«=12 

n=15 

P 

k 

'-i 

K9 

Ks 

K 

k 

.     * 

3 

k« 

Ks 

K 

.001 

.145 

92.5 

53.7 

19.1 

19.1 

.158 

94.7 

56.4 

19.1 

19.1 

.002 

.196 

93.5 

88.6 

37.4 

37.4 

.215 

92.8 

75.0 

37.1 

37.1 

.003 

.235 

92.2 

8L2 

55.3 

55.3 

.258 

91.4 

88.4 

54.8 

54.8 

.004 

.266 

91.1 

90.3 

72.9 

72.9 

.291 

90.3 

98.7 

72.2 

72.2 

.005 

.291 

90.3 

98.7 

90.3 

90.3 

.319 

89.4 

106.8 

89.4 

89.4 

.006 

.314 

89.6 

105.4 

107.5 

105.4 

.343 

88.5 

114.3 

106.2 

106.2 

.007 

.334 

88.9 

111.3 

124.5 

111.3 

.366 

87.8 

120.4 

122.9 

120.4 

.008 

.352 

88.3 

116.5 

141.2 

116.5 

.384 

87.2 

125.7 

139.5 

125.7 

.009 

.370 

87.7 

121.6 

157.9 

121.6 

.401 

86.6 

130.3 

155.9 

130.3 

.010 

.384 

87.2 

125.7 

174.4 

125.7 

.417 

86.1 

135.0 

172.2 

135.0 

.011 

.398 

86.7 

129.6 

190.7 

129.6 

.432 

85.6 

138.6 

188.3 

138.6 

.012 

.411 

86.3 

133.2 

207.1 

133.2 

.444 

85.2 

142.2 

204.5 

142.2 

.014 

.435 

85.5 

139.5 

239.4 

139.5 

.470 

84.3 

148.6 

235.6 

148.6 

.016 

.456 

84.8 

145.0 

271.4 

145.0 

.492 

83.6 

154.5 

267.6 

154.5 

.018 

.476 

84.1 

150.0 

302.8 

150.0 

.413 

82.9 

159.0 

298.4 

159.0 

.020 

.493 

83.6 

154.5 

334.4 

154.5 

.530 

82.3 

163.2 

329.2 

163.2 

.030 

.561 

81.3 

171. 

487.8 

171. 

.600 

80.0 

180.0 

480. 

180.0 

.040 

.610 

79.6 

183. 

636.8 

183. 

.650 

78.4 

191.4 

627. 

191.4 

.050 

.650 

78.3 

190. 

783.0 

190. 

.680 

77.4 

197.7 

774. 

197.7 

For  bulky  concrete  constructions,  such  as  bridge  abutments 
or  very  heavy  slab  floors,  EG  has  a  lower  value  and  in  such  cases 
we  make  n  =  20  or  even  more.  Table  XLI  is  calculated  for 
these  conditions. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


Ill 


TABLE  XLI. — VALUES  OF  K  FOR  VARIOUS  PROPORTIONS  OF  STEEL  USED 

WHERE   C=700,  AND  /=  16,000. 


»=10 

«=20 

p 

k 

"4 

Kc 

Ks 

K 

k 

'-f 

Kc 

Ks 

K 

.001 

.132 

.956 

44.2 

15.3 

15.3 

.181 

.879 

55.7 

14.06 

14.06 

.002 

.190 

.937 

62.3 

30.0 

30.0 

.246 

.836 

72.0 

26.8 

26.8 

.003 

.217 

.928 

70.5 

44.6 

44.6 

.292 

.805 

82.3 

38.6 

38,6 

.004 

.246 

.918 

79.0 

58.8 

58.8 

.328 

.781 

89.7 

50.0 

50.0 

.005 

.270 

.910 

86.0 

72.8 

72.8 

.358 

.761 

95.4 

60.9 

60.9 

.006 

.292 

.903 

92.3 

86.7 

86.7 

.384 

.744 

100.0 

71.4 

71.4 

.007 

.311 

.896 

97.5 

100.4 

97.5 

.407 

.729 

103.8 

81.6 

81.6 

.008 

.328 

.890 

102.2 

113.9 

102.2 

428 

.715 

108.1 

91.5 

91.5 

.009 

.344 

.885 

106.6 

127.4 

106.6 

.447 

.702 

109.8 

101.1 

101.1 

.010 

.358 

.881 

110.4 

140.9 

110.4 

.463 

.691 

112.0 

110.6 

110.6 

.011 

.372 

.876 

114.1 

154.2 

114.1 

.479 

.681 

114.2 

119.9 

114.2 

.012 

.384 

.872 

117.2 

167.4 

117.2 

.493 

.671 

115.8 

128.8 

115.8 

.014 

.389 

.870 

118.5 

194.9 

118.5 

.519 

.654 

118.8 

146.5 

11-8.8 

.016 

.428 

.857 

128.4 

219.4 

128.4 

.542 

.639 

121.2 

163.6 

121.2 

.018 

.446 

.851 

132.8 

245.1 

132.8 

.562 

.625 

122.9 

180.0 

122.9 

.020 

.463 

.846 

137.1 

270.7 

137.1 

.580 

.613 

124.4 

196.2 

124.4 

.030 

.531 

.823 

153.0 

395.0 

153.0 

.65 

.567 

129.0 

272.2 

129.0 

.040 

.580 

.807 

163.8 

516.5 

163.8 

.70 

.534 

130.8 

341.8 

130.8 

.050 

.618 

.794 

171.7 

635.2 

171.7 

.73 

.514 

131.3 

411.2 

131.3 

56-A. — T-Beams. 


56-B.  —  T-Beams. 


112  REINFORCED    CONCRETE. 

AS  =  total  net  area  of  reinforcement. 

Case  I.    When  the  neutral  axis  lies  in  the  flange:  use  the 
formulas  for  rectangular  beams. 

Case  II.    When    the   neutral    axis   lies  in  the  stem:  the  fol- 
lowing formulas  neglect  the   compression   in  the  stem: 

Position  of  neutral  axis: 

2ndAs  -f  bt* 


Position  of  resultant  compression 
Zkd—  2, 


=   2kd-t  ~  3 
Arm  of  resisting  couple 

id  =  d—z 
Fibre  stresses 

M 


Mkd  f*     k 


fc  ~  bt(kd—y*f)jd  ~    n  k—\ 

(For   approximate    results    the    formulas    for   rectangular 
beams  may  be  used.) 


BUILDING  DESIGN  AND  CONSTRUCTION. 


113 


The  following  formulas  take  into  account  the  compres- 
sion in  the  stem;  they  are  recommended  where  the  flange 
is  small  compared  with  the  stem. 

Position  of  neutral  axis 


kd-- 


•V— 


+  (b-b'} 


nA&+(b—  b'}  A2     nAs+  (b—b'}  t 


Position  of  resultant  compression 


Arm  of  resisting  couple 

jd  =  d—z 

Fibre  stresses 

M  2Mkd 


J*  ~  AJd  ~  [  (2kd—t 

III.  Beams  Reinforced  for  Compression. 


Fig.   56-C. — Beams  Reinforced  for  Compression. 
Position  of  neutral  axis 
k- 


114  REINFORCED   CONCRETE. 

where 

p'=  steel  ratio  for  compressive  steel 
d '  =  depth  to  center  of  compressive  steel 
fa=  compressive  unit  in  steel 
C=  total  compressive  stress  in  concrete 
C'=  total  compressive  stress  in  steel 

z=  depth  to  resultant  of  C  and  C' 
A's  =  area  of  compressive  steel 

Position  of  resultant  compression 


2  = 

Arm  of  resisting  couple 

Fibre  stresses 

6M 

Ic  =  — 


M 


k-* 

fs'  =  nfc*      d 


IV.  Shear  Bond  and  Web  Reinforcement.  —  In  the  follow- 
ing, 20  refers  only  to  the  bars  constituting  the  tension  re- 
inforcement at  the  section  in  question  and  jd  is  the  lever  arm 
of  the  resisting  couple  at  the  section. 

For   rectangular   beam 

V 


bjd 
V 


BUILDING  DESIGN  AND  CONSTRUCTION.        115 

where 

F  =  total  shear 

v  =  shearing  unit  stress 

u  =  bond  stress  per  unit  area  of  bar 

o  =  circumference  or  perimeter  of  bar 

2<?  =  sum  of  the  perimeters  of  all  bars 

(For  approximate  results  /  may  be  taken  at  %.) 

The  stresses  in  web  reinforcement  may  be  estimated  by 
means   of  the   following  formulas: 

Vertical  reinforcement 

/•=-£- 

id  • 

Reinforcement  inclined  at  45  degrees 


in  which  P  =  stress  in  single  reinforcing  member,  V 
=  proportion  of  total  shear  assumed  as  carried  by  the  re- 
inforcement, and  s  =  horizontal  spacing  of  the  reinforcing 
members. 

The  same  formulas  apply  to  beams  reinforced  for  com- 
pression as  regards  shear  and  bond  stress  for  tensile  steel. 

For  T-beams, 

V  V 

~b'jd  ~ 


(For  approximate  results  /  may  be  taken  at 
V.   Columns. 
Unit  Stresses 

P 

fs  =.  nfc 


116 


REINFORCED    CONCRETE. 


TABLE  XLI-A.— FOR  THE  DESIGN  OF  TEE  BEAMS. 
Good  Rock  Concrete.  /» =-50,000.  /c=2,700. 


t 

d 

Area  of  Steel 

Ultimate  Moment 

b 

10 

6,(.0122+.0232Z) 

6,(    3750+  9580  0 

.2306/Z—  6,/2 

11 

6,  (.0222+.  0232  I) 

6,(    7810+107500 

.2206/Z—  6,/2 

12 

6,(.0337+.0232Z) 

6,(  13200+11900  0 

.214W—  b,/2 

13 

6,(.0464+.0232Z) 

6,(  20160+13080  I) 

.2106/Z—  6,/2 

14 

6,  (.0600+.  02320 

6,(  28600+14250  I) 

.2056/Z—  6//2 

VA" 

15 

b,  (.0736+.  0232  I) 

b,(  38200+15400  I) 

.2Q2W—  bf/2 

16 

b,  (.0882+.  02320 

6/(  49500+16550  I) 

.200fe,Z—  6//2 

17 

b,  (.1030+.  02320 

b,(  62200+17700  0 

.  1986/Z—  6,/2 

18 

6,(.1182+.  02320 

6/(  76500+18850  0 

.  1966,Z—  6,/2 

19 

6,(.1336+.  02320 

6/(  92000+20050  I) 

.  196W—  6//2 

20 

6/(.1486+.  02320 

6/(108700+21200  I) 

.  1946/Z—  6/72 

10 

6,(.0035+.  02320 

b,(    1035+  92900 

.217W—  6,/2 

11 

6,(.0103+.0232Z) 

6/(    3430+104500 

.2056/Z—  6,/2 

12 

6,(.0195+.0232Z) 

b,(    7320+116100 

.  1966/Z—  67/2 

13 

6,(.0302+.0232Z) 

6/(  12600+12780  I) 

.  190W—  b,/2 

14 

b,  (.0424+.  02320 

b,(  19420+13920  0 

.  1866,Z—  6,/2 

15 

b,  (.0548+.  02320 

b,(  27500+15100  I) 

.1836,/—  6,/2 

4' 

16 

6,  (.0684  +.02320 

b,(  37250+16250  I) 

.  1796/Z—  6,/2 

17 

6,(.0824+.  02320 

b,(  48400+17400  0 

.1776/Z—  6//2 

18 

6,(.0964+.  02320 

6/(  60700+18600  I) 

.  1756//—  6//2 

19 

6,(.  11  12+.  02320 

b,(  74700+19750  0 

.  1736/Z—  6,/2 

20 

6,(.1264+.  02320 

6/(  90300+20900  0 

.1726^—6,72 

22 

6,(.  1564  +.02320 

fe,(125000+23200  0 

.1706/Z—  6,/2 

24 

6,(.1876+.0232Z) 

6,(166000+25500  I) 

,1686^—6,72 

26 

6,(.2160+.  02320   • 

b,  (209500+27900  0 

.1686,Z—  6,/2 

10 

6,(.  00004+  .  02320 

b,(        11+  9000  0 

.2126,Z—  6,/2 

11 

6,(.0027+.0232Z) 

6/(      880+10160  Z) 

.  1956,Z—  6,/2 

12 

6,(.0087+.0232Z) 

b,(    3120+113200 

.  1856,Z—  6,/2 

13 

6,(.0171+.  02320 

6/(    6880+12500  Z) 

.  1776,Z—  6,/2 

14 

6,(.  0271  +  .  0232  I) 

6/(  12020+13650  Z) 

.1726,Z—  6,/2 

15 

b,  (.0382+.  02320 

6/(  18560+14800  Z) 

.  1686,Z—  6,/2 

16 

6,(.0507+.0232Z) 

b,(  26800+16000  Z) 

.1646,Z—  6,/2 

4M" 

17 

6,  (.0033  +.02320 

6/(  36200+17120  Z) 

.1616,Z—  6,/2 

18 

b,  (.0770+.  02320 

b,(  47200+18300  Z) 

.  1596,Z—  6,/2 

19 

6,(.0909+.  02320 

6/(  59600+19460  Z) 

.  1576,Z—  bf/2 

20 

6,(.1050+.0232Z) 

6/(  73200+20600  Z) 

.  1566,Z—  6,/2 

22 

6,(.1342+.0232Z) 

fe,(105000+22920  Z) 

.  1546,Z—  6,/2 

24 

6,(.1650+.  02320 

6,(143000+25250  Z) 

.  1526,Z—  6,/2 

26 

6,(.1960+.  02220 

fc,(187000+27600  Z) 

.1516,Z—  6,/2 

28 

b,  (.2268+.  02320 

fe,(235400+29900  Z) 

.  1506,Z—  6//2 

30 

b,  (.2580+.  02320 

fc,  (290000+32200  Z) 

.  1496,Z—  6,/2 

12 

6X.0021+.  02320 

6/(      725+11050  Z) 

.1786,Z—  b,/2 

13 

b,  (.0073  +.02320 

b,(    2830+12200Z) 

.  1696,Z—  6,/2 

14 

6,(.0156+.  02320 

b,(    6430+13350  Z) 

.1626,Z—  6,/2 

15 

b,  (.0246+.  02320 

b,(  11550+145000 

.1576,Z-6,/2 

16 

6,(.0350+.  02320 

6/(  17900+15700  Z) 

.  1536,Z—  6,/2 

17 

6,(.0465+.0232Z) 

6/(  25750+16850  Z) 

.  1506,Z—  6,/2 

18 

&X.0590+.  02320 

b,(  35200+18000  Z) 

.  1476,Z—  6,/2 

5" 

19 

&X.0718+.  0232Z) 

6/(  45800+19200  Z) 

.  1456,Z-6,/2 

20 

6,(.0854+.  02320 

6/(  58200+20300  Z) 

.  1436,Z—  6,/2 

22 

6,(.1130+.  02320 

6/(  86700+22650  Z) 

.1416,Z—  6,/2 

BUILDING  DESIGN  AND  CONSTRUCTION.        117 


TABLE  XLI-A.— FOR  THE  DESIGN  oc  TEE  BEAMS— (Continued). 
Good  Rock  Concrete.  /.= 50,000.  /c=2,700. 


t 

d 

Area  of  Steel 

Ultimate  Moment 

b 

24 

6X-1426+.0232Z) 

6X121500+25000  Z) 

.1396/Z—  6,/2 

26 

6X.1726+.0232Z) 

fe,(161700+27300  Z) 

.  1376/Z—  6,/2 

28 

6X.2036+.  0232Z) 

6X208000+29600  Z) 

.1366,Z—  6,/2 

5 

30 

6,(.  2344+.  0232  I) 

6,(259000+31900  Z) 

.  1356/Z—  6//2 

32 

6X.2660+.0232Z) 

6X316200+34250  Z) 

.  1346,Z—  6//2 

34 

6X.2980+.0232Z) 

6,  (380000+36600  Z) 

.  1346/Z—  6,/2 

14 

6X-0062+.0232Z) 

&/(    2560+13050Z) 

.  1566/Z—  6,/2 

15 

6X.0132+.  02320 

&/(    6000+14200  Z) 

.  1506,Z—  6,/2 

16 

b,  (.0220+.  0232T; 

6,(  10900+15400  Z) 

.  1456/Z—  bf/2 

17 

b,  (.03  18+.  0232  Z) 

6,(  17100+16550  Z) 

.1416/Z—  6,/2 

18 

6X.0429+.  02320 

&/(  24800+17700  Z) 

.  1386/Z—  6,/2 

19 

6X.0550+.0232Z) 

6,(  34200+18900  Z) 

.  1366/Z—  6,/2 

20 

6,  (.0673+.  0232  I) 

6,(  44600+20000  Z) 

.  1336/Z—  6//2 

5K" 

22 

6X.0936+.  0224Z) 

6/(  70000+22350  Z) 

.  1306,Z—  6,/2 

24 

6,(.  121  6+.  0232  Z) 

6,001500+24700  Z) 

.  1286/Z—  bt/2 

26 

6X.1510+.0232Z) 

6X138800+27000  Z) 

.  1276,Z—  6,/2 

28 

6X.1816+.0232Z) 

6X182200+29300  Z) 

.  1256/Z—  6,/2 

30 

6X.2120+.  0232Z) 

6X230800+31600  Z) 

.  1246/Z—  6,/2 

32 

6X.2420+.0232Z) 

6X284000+34000  Z) 

.  1236,Z—  6,/2 

34 

b,(.  2736+.  0232  I) 

6X344000+36300  Z) 

.  1226,Z—  b,/2 

36 

b,  (.3050+.  0232  I) 

6X410000+38600  Z) 

.  1226/Z—  6//2 

16 

6X.0118+.0232Z) 

&/(    5630+15100  Z) 

.  1396,Z—  6//2 

17 

6X.0198+.  0232Z) 

6X  10300+16250  I) 

.  1346,Z—  b,/2 

18 

6X.0292+.0232Z) 

6X  16400+17420Z) 

.1316,Z—  b,/2 

19 

6X.0398+.  0232Z) 

6X  24100+18600  Z) 

.  1286^—6,72 

20 

6X.0510+.0232Z) 

6X  33050+19750  Z) 

.  1256/Z—  bf/2 

22 

6X.0756+.0232Z) 

6X  55400+22050  Z) 

.  122b,l—b,/2 

6" 

24 

6X.1028+.0232Z) 

6,(  84000+24400  Z) 

.  1206,Z—  b,/2 

26 

6X.1304+.  0232Z) 

6X117500+26700Z) 

.1186^—6,72 

28 

&X.1592+.  0232Z) 

6X157000+29050  Z) 

.1166,Z—  6,/2 

30 

6X.1892+.0232Z) 

6X202500+31400  Z) 

.1156,Z—  6,/2 

32 

6X.2190+.0232Z) 

6,  (253000+33700  Z) 

.1146,Z—  6,/2 

34 

6X.2506+.0232Z) 

6X31  1000+36000Z) 

.1136,Z—  6,/2 

36 

6X.2820+.0232Z) 

6X374000+38300  Z) 

.1136,Z—  bt/2 

38 

6/(.  3130+.  0232Z) 

6X441500+40700  Z) 

.1126,Z—  6,/2 

16 

&X.0007+.  0232Z) 

&,(      294+14520  Z) 

.  1336,Z—  6,/2 

17 

6X.0038+.0232Z) 

6X    1860+15700  Z) 

.  1276,Z—  6,/2 

18 

6/(.  0091  +.  0232  Z) 

&,(    4820+16830  Z) 

.  1226,Z—  6,/2 

19 

6X.0161+.  0232Z) 

6X    9200+18000  Z) 

.1186,Z—  6,/2 

20 

fc,(.0244+.  0232Z) 

&,(  15000+191500 

.1156,Z—  6,/2 

22 

6/(.0444+.0232Z) 

6X  31100+215000 

.1106/Z—  6,/2 

24 

6,(.0674+.  0232Z) 

6X  52800+23800  Z) 

.  1066,Z—  6,/2 

7" 

26 

fe/(.0930+.0232Z) 

6,(  80800+26100  Z) 

.  1046,Z—  6,/2 

28 

6,(.H96+.0232Z) 

6X1  14000+28450  Z) 

.  1026,Z—  bt/2 

30 

6,(.1470+.0232Z) 

6X152500+30750  Z) 

.1016,1—  bt/2 

32 

6/(.1760+.  0232Z) 

6,  (198000+33  100  Z) 

.1006/Z—  &,/2 

34 

6,(.2064+.0232Z) 

6X249500+35400  Z) 

.0996,Z—  bf/2 

36 

6,(.2360+.  0232/) 

&X305000+37700  Z) 

.0986,Z—  b,/2 

38 

6/(.2660+.0232Z) 

6X368000+40100  Z) 

.0976,Z—  6,/2 

40 

6/C.2970+.0232Z) 

6X434000+42400  Z) 

.0976/Z—  bt/2 

118 


REINFORCED    CONCRETE. 


TABLE  XLI-A.— FOR  THE  DESIGN  OP  TEE  BEAMS— (Continued). 
Good  Rock  Concrete.  .=50,000.  /c=2,700. 


/ 

d 

Area  of  Steel 

Ultimate  Moment 

b 

20 

6X.0071+.  0232Z) 

b,(    4140+186000 

.  1096/J!—  6,/2 

22 

6X.0206+.  02320 

b,(  13720+20900  Z) 

.  102W—  6,/2 

24 

6X.0390+.  02320 

b,(  29300+23200  0 

,0986/Z—  6,/2 

26 

6X.0604+.  0232Z) 

6,(  50600+25500  0 

.0956,*—  6,/2 

28 

6,(  .  0844+  .  0232  1)     I     6X  77600+27900  0 

.0936/f—  6,/2 

30 

&X.1096+.  02320 

6,(1  10200+30200  I) 

.0916,^—6,72 

32 

6,(.13t>8+.  02320 

6X149200+32500  I) 

.0906,^—  6,/2 

8" 

34 

6X.1646+.  02320 

&/U93300+34800  0 

.0886,Z—6,/2 

36 

6X.1928+.  02320 

&,(243000+37200  I) 

.0876,Z—  6,/2 

38 

6,(.  2224+.  02320 

6X299000+39500  0 

.0866,?—  6,/2 

40 

b,(.  2526+.  02320 

6X361000+41800  0 

.0866,Z—  6,/2 

42 

6X.2820+.  02320 

6X426500+44200  0 

.0856,Z—6,/2 

44 

6X.3130+.  02320 

6,  (500000+46500  0 

.0856,Z—  6,/2 

46 

6X.3430+.0232Z) 

6X578000+48750  I) 

.0846,Z—  6,72 

48 

6X.3760+.  02320 

6X664000+51100  0 

.0846,i-6,/2 

Parabolic    Line    Formula. — Assumptions    for    New    York. 
(See  Fig.  57.) 


Fig.    57. — Parabolic   Line   Diagram. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


119 


500  Ibs.  per  sq.  in. 
50  Ibs.  per  sq.  in. 
16,000  Ibs.  per  sq.  in. 
10 


K 
Av 


pn) (15) 

(16) 

(17) 

(18) 

(19) 

Pft  (1  —  f^) (20) 

the  smaller  of  the  two  values  A"c 
and  AS 

z/(l  —  f£) (21) 


TABLE  XLII—  VALUES  OF  K  FOR  VARIOUS  PROPORTIONS  OF  STEEL  USED 
WHEN  /c=500  AND  /»=16,000. 


p 

k 

H* 

Kc 

Ks 

K 

** 

.001 

.115 

.954 

36.6 

15.3 

15.3 

47.7 

.002 

.159 

.936 

49.6 

30.0 

30.0 

46.8 

.003 

.191 

.924 

58.7 

44.3 

44.3 

46.2 

.004 

.217 

.913 

66.0 

58.3 

58.3 

45.6 

.005 

.239 

.904 

72.0 

72.4 

72.0 

45.2 

.006 

.258 

.897 

77.2 

86. 

77.2 

44.8 

.007 

.276 

.890 

81.8 

99. 

81.8 

44.5 

.008 

.292 

.883 

85.9 

113. 

85.9 

44.2 

.009 

.306 

.878 

89.5 

126. 

89.5 

43.9 

.010 

.320 

.872 

92.9 

139. 

92.9 

43.6 

.012 

.344 

.862 

98.8 

165.6 

98.8 

43.  * 

.014 

.365 

.854 

103.9 

191.3 

103.9 

42.7 

.016 

.384 

.846 

108.4 

216.6 

108.4 

42.3 

.018 

.402 

.839 

112.4 

241.7 

112.4 

42.0 

.020 

.418 

.833 

116.0 

266.5 

116.0 

41.6 

.030 

.483 

.807 

129.8 

387.4 

129.8 

40  4 

.040 

.631 

.788 

139.3 

504.2 

139.3 

39.4 

.060 

.669 

.772 

146.4 

618.0 

146.4 

38.6 

120 


REINFORCED   CONCRETE. 


TABLE  XLIII. — VALUES  OP  K  FOR  VARIOUS  PROPORTIONS  OP  STEEL  USED 
WHEN  f*=750.  a=75,  /•-aO.OOO. 


n=12 

M=15 

P 

k 

'-!* 

Kc 

Ka 

K 

*v 

k 

-I* 

Kc 

K3 

K 

^v 

.001 

.125 

.950 

57.2 

19.0 

19.0 

71.2 

.137 

.945 

64.7 

18.9 

18.9 

70.9 

.002 

.173 

.931 

80.5 

37.2 

37.2 

69.8 

.161 

.936 

75.3 

37.4 

37.4 

70.2 

.003 

.207 

.917 

94.5 

55.0 

55.0 

68.8 

.228 

.909 

103.6 

54.5 

54.5 

68.2 

.004 

.235 

.906 

106.0 

72.5 

72.5 

67.9 

.258 

.897 

115.7 

71.8 

71.8 

67.3 

.005 

.258 

.897 

115.7 

89.7 

89.7 

67.3 

.284 

.886 

125.8 

88.6 

88.6 

66.4 

.006 

.279 

.888 

123.4 

106.6 

106.6 

66.6 

.308 

.877 

135.0 

105.2 

105.2 

65.8 

.007 

.297 

.881 

130.4 

123.3 

123.3 

66.1 

.326 

.870 

141.8 

121.8 

121.8 

65.2 

.008 

.314 

.874 

137.2 

139.8 

137.2 

65.5 

.342 

.863 

147.6 

138.1 

138.1 

64.7 

.009 

.329 

.868 

142.4 

156.2 

142.4 

65.1 

.360 

.856 

154.1 

154.1 

154.1 

64.2 

.010 

.344 

.862 

148.3 

172.4 

148.3 

64.6 

.375 

.850 

159.4 

170.0 

159.4 

63.7 

.012 

.369 

.852 

156.8 

204.5 

156.8 

63.9 

.402 

.839 

168.7 

201.4 

168.7 

62.9 

.014 

.392 

.843 

165.2 

236.0 

165.2 

J63.2 

.425 

.830 

176.4 

232.4 

176.4 

62.2 

.016 

.412 

.835 

172.0 

267.2 

172.0 

62.6 

.446 

.822 

183.3 

253.0 

183.3 

61.6 

.018 

.430 

.828 

178.0 

298.1 

178.0 

62.1 

.465 

.814 

189.3 

293.0 

189.3 

61.0 

.020 

.446 

.822 

183.3 

328.8 

183.3 

61.6 

.482 

.807 

194.5 

322.8 

194.5 

60.5 

.030 

.513 

.795 

203.5 

477.0 

203.5 

59.6 

.551 

.780 

214.5 

468. 

214.5 

58.5 

.040 

.562 

.775 

217.8 

620.0 

217.8 

58.1 

.600 

.760 

228.0 

608. 

228.0 

57.0 

.050 

.599 

.760 

228.0 

760.0 

228.0 

57.0 

.638 

.745 

237.6 

745. 

237.6 

55.8 

Maximum  Bending  Moment  in  Slabs. — In  Table  XLIV, 
giving  maximum  bending  moment  in  slabs  according  to 
straight  line  formula,  the  assumptions  are: 

/c=500  Ibs.  per  sq.  in. 
n  =  12. 
•  Fireproofing  —  1  in. 

in  thousands  of  in.  Ibs. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


121 


TABLE  XLIV. — MAXIMUM  BENDING  MOMENTS  IN  SLABS  ACCORDING  TO 
STRAIGHT  LINE  FORMULA. 


Steel  Sizes. 

Slab  Sizes  in  inches. 

Diameter 
in  ins. 

Spacing 
in  ins. 

3 

3* 

4 

41 

5 

5i 

6 

H 

1 

1 

1 
1 
1 

6 
5 
4 

6 
5 
4 
3 
2J 

0 
5 
4 
3 

n 

6 
5 
4 
3 

M 

6 
5 
4 
3 

6 
5 
4 

6 
5 
4 

2.8 
3.2 
3.4 

3.4 
3.8 
4.0 
4.3 
4.6 

3.9 
4.2 
4.4 

3.6 
4.4 
5.0 

5.0 
5.4 

5.8 
6.3 
6.8 

5.6 
6.1 
6.5 
7.0 
7.5 

6.3 
6.7 
7.2 

7.7 

4.3 
5.4 
6.2 

6.3 
7.3 
8.0 
8.7 
9.2 

7.7 
8.3 
8.8 
9.6 
10.2 

8.6 
9.1 
9.6 
10.6 

5.2 
6.2 
7.3 

7.4 
9.0 
10.2 
11.2 
11.9. 

10.0 
10.6 
11.4 
12.7 
13.4 

10.9 
11.9 
12.6 
13.7 
14.7 

9.0 
11.1 
12.4 
13.8 
14.9 

12.4 
13.3 
14.1 
15.5 
16.5 

13.7 
14.8 
15.8 
17.2 
18.4 

15.0 

16.1 
17.1 

9.7 
12.5 
14.7 
16.8 
18.0 

14.4 
15.6 
17.3 
18.9 
20.4 

16.9 
18.0 
19.2 
21.0 
22.4 

18.1 

19.6 
21.0 
22.9 

16.9 
20.2 
21.2 

15.5 
18.4 
20.7 
22.6 
24.5 

20.0 
21.2 
22.8 
25.1 
26.8 

21.7 
23.4 
25.0 
27.2 

23.5 
25.5 
26.8 

18.0 

21.8 
24.4 
26.2 
28.0 

23.1 

24.6 
26.7 
29.5 
31.7 

25.4 

27.2 
29.0 
31.8 

27.3 
30.5 
31.7 

39.2 
31.8 
33.3 

The  American  Wire  Fence  Co.,  Chicago,  who  control  the  Ameri- 
can system  of  reinforcing,  have  designed  and  executed  a  large 
number  of  buildings,  basing  their  floor  slab  dimensions  on  Table 
XLTV,  in  which  the  following  assumptions  are  made: 

(1)  One   layer   of   4xl2-in.   mesh    high-carbon   fabric   of  No.    5 
carrying  wires  and  No.  11  distributing  wires. 

(2)  High    carbon   steel   rods   in   addition   to   the   fabric   where 
shown. 

(3)  A  1  to  6  graded  mixture  of  Portland  cement,  sand  and  peb- 
bles or  hard   stone  crushed  to  pass  through  a  %-in.   mesh  screen, 
proportioned  to  give  a  maximum  density   (see  page  21.) 

(4)  All  spans  continuous  in  one  direction. 

Example. — For  a  9-ft.  span  with  a  live  load  of  150  Ibs.  per  sq. 
ft.  over  and  above  the  dead  load  we  require  one  layer  of  fabric  and 
a/4-in.  rods  spaced  G1^  ins.  on  centers  in  a  4-in.  slab. 


122 


REINFORCED    CONCRETE. 


g 

*^7 

00  CO 

0510 
1 

05UT3 

o?1^ 

Sj. 

00 

s* 

2l 

s 

»i 

£7 

£? 

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05^5 

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27 

OCO 

T-l      1 

oo 

«H 

CO? 
Hn 

"1 

"1 

w! 

*-  •> 

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07 

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05 

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0500 

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g, 

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1005 

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mfoo 

>o£ 

,*4c* 

0 

CO-H 

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s? 

«H> 

Hn 

H«^T 

05 
"3    1 

«f» 

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who 

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CO    1 

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to 

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45 

"1 

"1 

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roi 

CO(M 

-7 

O5 

h 

^§ 

II 
11 

spacing  of 
rods. 

Slab  thickness. 
Reinforcement 

Slab  thickness 
Reinforcement 

Slab  thickness 
Reinforcement 

Slab  thickness 
Reinforcement 

Slab  thickness 
Reinforcement 

Slab  thickness 
Reinforcement 

Slab  thickness 
Reinforcement 

Slab  thickness 
Reinforcement 

Slab  thickness 
Reinforcement 

|l-s 

£&1 

§ 

£ 

o 

3 

0 
US 

>o 

0 

0 

0 

o 

CO 

BUILDING  DESIGN  AND  CONSTRUCTION.         123 

TABLE  XLV— A. 


Spacing. 


Spacing  of  Round  Rods  for  Given  Area  per  1  Ft.  Wide. 


Dia.  Rods 

y± 

%> 

H 

/& 

y% 

% 

% 

% 

3'  f 

.196 

.307 

.441 

.601 

.785 

.994 

1.227 

1.485 

1.767 

2.405 

3.142 

.168 

.263 

.378 

.515 

.673 

.852 

1.052 

1.272 

1.514 

2.061 

2.692 

4'2 

.147 

.230 

.331 

.451 

.589 

.745 

.920 

1.113 

1.325 

1.804 

2.356 

4H* 

.131 

.204 

.294 

.401 

.523 

.663 

.818 

.990 

1.178 

1.603 

2.094 

5'  f 

.118 

.184 

.265 

.361 

.471 

.596 

.736 

.891 

1.060 

.443 

.885 

.107 

.167 

.240 

.327 

.428 

.542 

.669 

.809 

.963 

.311 

.712 

6  2 

.098 

.153 

.221 

.300 

.392 

.497 

.613 

.742 

.883 

.202 

.571 

6H* 

.090 

.141 

.204 

.277 

.362 

.458 

.566 

.685 

.815 

.110 

.450 

7' 

.084 

.131 

.189 

.257 

.336 

.426 

.526 

.636 

.757 

.030 

.346 

7}^ 

.078 

.123 

.176 

.240 

.314 

.397 

.441 

.594 

.707 

.962 

.256 

8* 

.073 

.115 

.165 

.225 

.294 

.373 

.460 

.557 

.663 

.902 

.178 

9' 

.066 

.102 

.146 

.200 

.262 

.330 

.405 

.495 

.590 

.800 

.050 

10* 

.058 

.091 

.132 

.180 

.235 

.297 

.365 

.445 

.530 

.720 

.940 

12' 

.049 

.076 

.110 

.150 

.196 

.248 

.306 

.371 

.442 

.601 

.785 

14' 

.042 

.065 

.094 

.128 

.167 

.212 

.263 

.318 

.376 

.515 

.665 

16' 

.037 

.057 

.082 

.112 

.146 

.185 

.230 

.277 

.330 

.450 

.585 

TABLE  XLV— B. 


Spacing. 


Weight  of  Round  Rods  per  1  Ft.  Width  for  Given  Spacing. 


dia. 

*• 

V 

H' 

£ 

H* 

V  |  K- 

%" 

*' 

H* 

r 

3' 

.666 

1.044 

1.50 

2.044 

2.667 

3.38 

4.172 

5.048 

6.008 

8.176 

10.68 

3^* 

.568 

.895 

1.287 

.755 

2.287 

2.897 

3.576 

4.327 

5.15 

7.008 

9.154 

4' 

.500 

.783 

1.125 

.533 

2.000 

2.535 

3.193 

3.786 

4.506 

6.132 

8.000 

4M* 

.444 

.696 

1.000 

.362 

.778 

2.254 

2.782 

3.366 

4.006 

5.450 

7.120 

5» 

.400 

.626 

.900 

.226 

.600 

2.028 

2.500 

3.029 

3.605 

4.906 

6.400 

5^* 

.364 

.570 

.818 

.115 

.455 

1.825 

2.275 

2.753 

3.277 

4.412 

5.827 

6' 

.333 

.522 

.750 

.022 

.333 

.690 

2.086 

2.524 

3.004 

4.088 

5.340 

6J-4' 

.307 

.482 

.693 

.944 

.231 

.561 

.925 

2.330 

2.780 

3.732 

4.929 

7' 

.285 

.447 

.643 

.876 

.143 

.448 

.788 

2.163 

2.575 

3.465 

4.577 

7V6* 

.266 

.418 

.600 

.818 

1.067 

.352 

.669 

2.019 

2.403 

3.234 

4.272 

8* 

.250 

.392 

.563 

.767 

1.000 

.268 

.565 

.893 

2.253 

3.066 

4.000 

9' 

.222 

.348 

.500 

.681 

.889 

1.127 

.391 

.683 

2.003 

2.725 

3.560 

10' 

.200 

.313 

.450 

.613 

.800 

1.014 

.251 

.519 

1.803 

2.453 

3.200 

12' 

.167 

.261 

.375 

.511 

.667 

.845 

.043 

.262 

1.502 

2.044 

2.670 

14' 

.143 

.224 

.332 

.438 

.572 

.724 

.894 

.082 

1.288 

1.733 

2.289 

16' 

.126 

.196 

.282 

.384 

.500 

.634 

.783 

.947 

1.127 

1.533 

2.000 

1 

124 


REINFORCED    CONCRETE. 


TABLE  XLV-C. 
(New  Style  Bar) 


Spacing. 


Spacing  of  Corrugated  Square  Bars  for  Given  Area  per  1  Foot  Width. 


Size  of  Bar. 

%* 

1-3* 

W 

%" 

%" 

%" 

1" 

IH' 

2" 

.360 

.66 

1.50 

2.34 

3.36 

4.62 

6.00 

9.37 

2H" 

.29 

.53 

1.20 

1.87 

2.69 

3.70 

4.80 

7.50 

3" 

.24 

.44 

1.00 

1.56 

2.24 

3.08 

4.00 

6.24 

3^" 

.21 

.38 

.86 

1.34 

.92 

2.64 

3.43 

5.36 

4" 

.18 

.33 

.75 

1.17 

.68 

2.31 

3.00 

4.68 

4H" 

.16 

.29 

.67 

1.04 

.49 

2.05 

2.67 

4.16 

5" 

.14 

.26 

.60 

.94 

.34 

1.85 

2.40 

3.75 

5M" 

.13 

.24 

.55 

.85 

.22 

1.68 

2.18 

3.41 

6" 

.12 

.22 

.50 

.78 

.11 

1.53 

2.00 

3.12 

6H" 

.11 

.20 

.46 

.72 

1.03 

1.42 

1.85 

2.88 

7* 

.10 

.19 

.43 

.67 

.96 

1.32 

1.72 

2.68 

71A" 

.10 

.18 

.40 

.62 

.89 

1.23 

1.60 

2.50 

8" 

.09 

.17 

.38 

.59 

.84 

1.15 

1.50 

2.34 

8^" 

.08 

.16 

.35 

.55 

.79 

1.09 

1.42 

2.20 

9* 

.08 

.15 

.33 

.52 

.75 

1.02 

1.33 

2.08 

9K" 

.08 

.14 

.32 

.49 

.71 

.97 

1.26 

1.97 

10' 

.07 

.13 

.30 

.47 

.67 

.92 

1.20 

1.87 

11" 

.07 

.12 

.27 

.43 

.61 

.84 

1.09 

1.70 

12" 

.06 

.11 

.25 

.39 

.56 

.77 

1.00 

1.56 

TABLE  XLV-D. 


Size. 

Weight 
in  Lbs. 
per  Foot. 

Peri- 
meter. 

Areas  of  Square  Bars. 

Number  of  Rods. 

1 

2 

3 

4 

5 

6 

7 

8 

9 

H' 

.212 

1.00 

.063 

.125 

.187 

.250 

.313 

.375 

.438 

.500 

.565 

%," 

.332 

1.25 

.098 

.195 

.293 

.391 

.489 

.586 

.684 

.782 

.879 

%' 

.478 

1.50 

.141 

.282 

.422 

.562 

.703 

.844 

.984 

1.125 

1.265 

%,' 

.651 

1.75 

.191 

.383 

.574 

.766 

.957 

1.148 

1.340 

1.531 

1.723 

y* 

.850 

2.00 

.250 

.500 

.750 

1.000 

1.250 

1.500 

1.750 

2.000 

2.250 

%' 

1.076 

2.25 

.316 

.632 

.949 

1.266 

1.583 

1.898 

2.215 

2.532 

2.848 

5A" 

1.328 

2.50 

.391 

.781 

1.172 

1.562 

1.953 

2.344 

2.734 

3.125 

3.515 

%' 

.     1.C07 

2.75 

.473 

.945 

1.418 

1.892 

2.364 

2.836 

3.309 

3.782 

4.254 

%' 

1.913 

3.00 

.563 

1.125 

1.618 

2.250 

2.813 

3.375 

3.938 

4.500 

5.053 

%* 

2.245 

3.25 

.660 

1.320 

1.981 

2.641 

3.301 

3.961 

4.621 

5.282 

5.942 

y&' 

2.603 

3.50 

.766 

1  531 

2.297 

3.062 

3.828 

4.594 

5.359 

6.125 

6.890 

%" 

2.988 

3.75 

.879 

1.758 

2.637 

3.516 

4.395 

5.273 

6.152 

7.031 

7.910 

r 

3.400 

4.00 

1.000 

2.000 

3.000 

4.000 

5.000 

6.000 

7.000 

8.000 

9.000 

\%," 

3.838 

4.25 

1.129 

2.258 

3.387 

4.516 

5.645 

6.773 

7.903 

9.031 

10.160 

VA" 

4.303 

4.50 

1.266 

2.531 

3.797 

5.062 

6.328 

7.594 

8.859 

10.125 

11.390 

ifc' 

4.795 

4.75 

1.410 

2.820 

4.231 

5.641 

7.051 

8.461 

9.871 

11.281 

12.692 

IK* 

5.313 

5.00 

1.563 

3.125 

4.688 

6.250 

7.813 

9.375 

10.938 

12.500 

14.063 

i« 

5.857 

5.25 

1.723 

3.445 

5.168 

6.891 

8.614 

10.336 

12.059 

13.782 

15.504 

W 

6.428 

5.50 

1.891 

3.781 

5.672 

7.562 

9.453 

11.344 

13.234 

15.125 

17.015 

1%' 

7.026 

5.75 

2.067 

4.133 

6.199 

8.266 

10.332 

12.398 

14.465 

16.531 

18.598 

VA' 

7.650 

6.00 

2.250 

4.500 

6.750 

9.000 

11.250 

13.500 

15.750 

18.000 

20.250 

BUILDING  DESIGN  AND  CONSTRUCTION.         125 

BEAMS  AND  GIRDERS. 

Whenever  a  slab  floor  construction  becomes  too  heavy 
owing  to  large  span  and  load,  beams  are  introduced  and  in 
most  cases  built  monolithic  with  the  floor  slabs,  so  that  for 
calculation  purposes  the  beams  may  be  considered  as  tee- 
beams.  The  area  above  the  neutral  axis  is  then  relied  upon 
to  take  care  of  the  compressive  stresses,  while  the  tension 
is  taken  up  by  the  steel  reinforcement  placed  below  the 
neutral  axis  in  the  web.  There  is  as  great  a  number  of 
beam  systems  as  floor  slab  systems,  and  before  entering  upon 
the  calculation  of  typical  floors  and  beams  a  number  of  the 
better  known  systems  will  be  described.  Beams  are  classed 
as  loose  rod  systems  or  frame  systems. 

Loose  Rod  Systems. — Loose  rods  for  reinforcing  beams 
were  formerly  employed  exclusively,  but  more  recent  prac- 
tice has  shown  the  advisability  of  tying  the  reinforcing  mem- 
bers rigidly  together  before  placing  them  in  the  mold.  This 
latter  method  is  used  very  extensively  in  American  prac- 
tice, while  the  loose  rod  method  is  preferred  abroad.  This 
difference  between  American  and  foreign  practice  is  tracea- 
ble directly  to  the  difference  in  conditions  governing  the 
work.  In  America,  where  labor  is  higher,  rapidity  in  erec- 
tion becomes  an  important  feature,  and  the  time  cannot  be 
spent  in  the  field  for  careful  placing  of  reinforcement,  hence 
the  utility  of  having  the  reinforcement  arrive  in  the  field 
in  an  assembled  state.  The  following  are  some  of  the  more 
important  loose  rod  systems: 

The    Hennebique    system    uses    two    round    rods    with    split 
ends,  one  rod  being  straight  and  the  other  bent  upward  at 
a  point  about  one-third  of  the  span  from  the  supports  for 
the  purpose  of  resisting  the  shearing  stresses  at  the  ends. 
Another  feature  is  the  use  of  hoop  iron  stir- 
rups  (Fig.  58)   at  intervals  to  strengthen  the 
beam  against  horizontal  shear  or  diagonal  ten- 
sion.   Both  bars  are  included  within  the  same 
stirrup,  but  in  some  forms  of  construction  the 
bique  System.       bent  and    straight  bars   are  used   alternately. 


126 


REINFORCED    CONCRETE. 


For  heavy  construction,  compression  reinforcement  is  also  re- 
sorted to,  and  in  this  case  stirrups  are  placed  outside  of  these 
rods  and  extend  downward  into  the  concrete. 

'The  Coularou  system,  Fig.  59,  has  stirrups  inclined  at  45° 
and  their  spacing  increases  from  the  supports  toward  the 
middle  of  the  span.  Each  stirrup  is  hooked  around  upper 
and  lower  reinforcement,  and  near  the  middle  of  the  beam 


Fig.  59. — Coularou  Beam  Reinforcement. 

the  upper  reinforcement  is  bent  down  at  an  angle  of  45°  and 
joins  the  lower  bar,  parallel  to  the  same  over  the  central 
portion  of  the  beam. 

The  Locher  beam  consists  of  a  number  of  round  or  flat 
bars  of  different  length,  having  their  middle  portion  straight 
and  being  curved  up  at  the  ends,  with  the  intention  of  being 
as  nearly  as  possible  normal  to  the  direction  of  the  maximum 
tensile  stresses,  thereby  decreasing  the  tendency  toward  slid- 
ing or  slipping  along  the  length  of  the  reinforcement. 

The  Coignet  system,  Fig.  60,  has  upper  and  lower  bars 
connected  by  a  light  hoop  iron  web  fastened  alternately  to 
the  upper  and  lower  bars,  thus  forming  a  light  truss. 


Fig.    60. — Coignet  Beam   Reinforcement. 


BUILDING  DESIGN  AND  CONSTRUCTION.        127 

Frame  Systems. — Various  styles  of  reinforcement  for 
frame  systems  are  illustrated  by  Figs.  20  to  25.  In  addition 
to  having  the  beam  and  girder  reinforcement  tied  rigidly 
together,  it  is  customary  with  most  of  these  systems,  to  tie 
the  columns  and  slabs  reinforcement  to  that  in  the  beams 
and  girders,  thus  having  all  the  steel  reinforcement  in  the 
building  tied  together.  As  much  as  possible  of  the  fastening 
together  is  done  before  insertion  in  the  forms,  thus  reduc- 
ing to  a  minimum  the  liability  of  wrongly  placing  the  steel. 

Tables  of  Safe  Loads  and  Steel  Areas  for  Beams. — From 
formulas  evolved  by  Prof.  Talbot,  given  on  p.  94,  from  Univ.  of 
111.  Bulletin,  Feb.  1,  1907,  the  following  rules  are  deduced : 

(1)  For  area  of  cross-section  of  steel  reinforcement  for 
other  widths  of  beam  multiply  by  the  width  in  inches. 

(2)  Total  loads  for  other  spans  and  the  same  depth  of 
steel  are  inversely  proportional  to  the  spans. 

(3)  Total  loads  for  other  depths  of  steel  and  the  same 
span  are  directly  proportional  to  the  squares  of  the  depths. 

By  using  the  above  mentioned  formulas,  Tables  XLVI  to 
LI,  similar  to  those  given  in  Concrete,  Plain  and  Reinforced, 
by  Taylor  and  Thompson,  have  been  calculated,  using  different 
values  for  K%  p,  fc  and  fs. 

Some  writers  prefer  to  use  ultimate  loads  and  ultimate 
moments.  Considerable  economy  in  construction  is  often 
found  by  using  4LL  -f-  2DL,  where  LL  =  live  load,  and  DL 
—  dead  load. 

For  instance,  for  a  roof 

4  X  40  =  160  Ibs.  per  sq.  ft.  LL 
2  X  50  =  100  Ibs.  per  sq.  ft.  DL 
Total 260  Ibs.  per  sq.  ft. 

Then  the  elastic  limits  of  steel  and  concrete  are  used  in- 
stead of  the  values  given  for  fs  and  fc. 


128 


REINFORCED    CONCRETE. 


TABLE  XLVI. — SAFE  LOADS  AND  STEEL  AREAS  FOR  BEAMS. 


a 

1 

« 

«+-* 

Sal 

e  loac 

in  Ib 

3.  per 

linear 

ft.  of 

beam 

1  inc 

i  wide 

0 
A 
& 

0) 

Span  i 

n  feet 

• 

Q 

ft  ins. 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

5 

44 

30 

22 

17 

13 

11 

9 

8 

...... 

6 

68 

47 

35 

27 

21 

17 

15 

12 

"16" 

..... 

7 

98 

68 

50 

38 

30 

25 

20 

17 

15 

13 

"io" 

8 

134 

93 

68 

52 

41 

33 

28 

23 

20 

17 

15 

13 

9 

164 

114 

84 

64 

51 

41 

34 

28 

24 

21 

19 

16 

10 

209 

145 

106 

82 

64 

52 

43 

36 

31 

27 

23 

20 

11 

259 

180 

132 

101 

80 

65 

54 

45 

38 

33 

29 

25 

12 

315 

219 

161 

123 

97 

79 

65 

55 

47 

40 

35 

31 

13 

360 

250 

184 

141 

111 

90 

74 

63 

53 

46 

40 

35 

14 

426 

296 

217 

166 

131 

106 

88 

74 

63 

54 

47 

42 

15 

497 

345 

253 

194 

153 

124 

103 

86 

73 

63 

55 

48 

16 

573 

398 

292 

224 

177 

143 

118 

99 

85 

73 

64 

56 

17 

655 

455 

334 

256 

202 

164 

135 

114 

97 

84 

73 

64 

18 

742 

515 

379 

290 

229 

185 

153 

129 

110 

95 

82 

72 

19 

788 

547 

402 

308 

243 

197 

163 

137 

116 

100 

88 

77 

20 

613 

451 

345 

272 

221 

182 

153 

131 

113 

98 

86 

22 

757 

556 

426 

336 

273 

225 

189 

161 

139 

121 

106 

24 

673 

515 

407 

330 

272 

229 

195 

168 

147 

129 

26 

613 

484 

392 

324 

272 

232 

200 

174 

153 

28 

720 

569 

461 

381 

320 

272 

235 

205 

180 

30 

660 

534 

441 

371 

316 

273 

237 

209 

36 

765 

632 

531 

452 

390 

340 

300 

42 

738 

629 

542 

472 

415 

48 

720 

627 

551 

Proportions,  1:6:  steel  reinforcement,  0.8  percent;  K=  102.2;  £=3,000,000. 
/t  =  depth  of  beam;  n=-10;  /, - 700 ;/,=-  14,000;  6=1;  d=* depth  of  steel  from 
top  of  beam. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


129 


TABLE  XLVI   (Continued). — SAFE  LOADS  AND  STEEL  AREAS  FOR  BEAMS. 


Safe  load  in  Ibs.  per  linear  ft.  of  beam 
1  inch  wide. 

ll43! 

3  . 

^3T3 

| 

J3 

H 

CTiTJ      . 

PI 

loment 
stance. 

«« 

*+•<          .  i^H 

~O«-*J 

*% 

H-a 

o 

..s  % 

Q  W 

•a-0 

!fv4«H 

£% 

^3 

Span  in  ft. 

£~* 

B 

Q 

"V 

$"3 

O. 

Q 

d 

sq. 

h 

17 

18 

19 

20 

25 

30 

35 

Ibs. 

ins. 

ins. 

ins. 

M 

ms. 

5.3 

4.0 

.0 

.032 

1,635 

5 

6.3 

5.0 

.0 

.040 

2,555 

6 

7  4 

6  0 

o 

048 

3  679 

7 

12 

8.5 

7.0 

.0 

.056 

5,008 

8 

14 

9.5 

7.75 

.25 

.062 

6,138 

9 

18 

16 

14 

13 

10  6 

8.75 

25 

070 

7  825 

10 

22 

20 

18 

16 

11.6 

9.75 

.25 

.078 

9J15 

11 

27 

24 

22 

20 

12  7 

10  75 

.25 

086 

11  810 

31 

28 

25 

23 

13.8 

11.5 

.5 

.092 

13,516 

13 

37 

33 

29 

27 

14.8 

12.5 

.5 

.10 

15  ,969 

14 

43 

38 

34 

31 

20 

15.9 

13.5 

.5 

.108 

18  ,626 

15 

50 

44 

40 

36 

23 

16  9 

14  5 

5 

116 

21  487 

16 

57 

51 

45 

41 

26 

18  0 

15^5 

.5 

'.124 

24  !513 

17 

64 

57 

51 

46 

30 

"2i" 

19.1 

16.5 

.5 

.132 

27  ,824 

18 

68 

61 

55 

49 

31 

22 

20.1 

17.0 

2.0 

.136 

29  ,536 

19 

76 

68 

61 

55 

35 

25 

21.2 

18.0 

2.0 

.144 

33,113 

20 

94 

84 

75 

68 

44 

30 

"22" 

23.3 

20.0 

2.0 

.160 

40,880 

22 

114 

102 

91 

82 

53 

37 

27 

25.4 

22.0 

2.0 

.176 

49  ,465 

24 

136 

121 

109 

98 

63 

44 

32 

27.6 

24.0 

2.0 

.192 

58,867 

26 

159 

142 

128 

115 

74 

51 

38 

29.7 

26.0 

2.0 

.208 

69  ,087 

28 

185 

165 

148 

133 

85 

59 

44 

31.8 

28.0 

2.0 

.224 

80,125 

30 

264 

236 

212 

191 

122 

85 

62 

38.1 

33.5 

2.5 

.268 

114  ,694 

36 

368 

328 

294 

266 

170 

118 

87 

44.5 

39.5 

2.5 

.316 

159  ,457 

42 

488 

435 

391 

353 

220 

157 

115 

50.9 

45.5 

2.5 

.364 

211  ,579 

48 

M-- 


wln-  X  12 


•  Kbd*. 


130 


REINFORCED   CONCRETE. 


TABLE  XLVII. — SAFE  LOADS  AND  STEEL  AREAS  FOR  BEAMS. 


B 

1 

Safe 

:  load 

in  Ibs 

.  per 

linear 

ft.  of 

beam 

1  incl 

i  wide 

o 
,c 

a 

& 

s 

pan  in 

feet. 

h 

ins. 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

5 

37 

26 

19 

14 

11 

9 

g 

6 

58 

40 

29 

22 

18 

14 

12 

10 

9 

...... 

7 

83 

58 

42 

32 

26 

21 

17 

14 

12 

'"9" 

8 

113 

79 

58 

43 

35 

28 

23 

20 

17 

14 

13 

ii 

9 

139 

97 

71 

54 

43 

35 

29 

24 

20 

18 

15 

14 

10 

177 

123 

91 

69 

54 

44 

37 

31 

26 

23 

20 

17 

11 

220 

153 

112 

86 

68 

55 

45 

38 

32 

28 

24 

21 

12 

267 

186 

136 

104 

82 

67 

55 

46 

39 

34 

30 

26 

13 

305 

212 

156 

119 

94 

76 

63 

53 

45 

39 

34 

30 

14 

361 

255 

184 

141 

111 

90 

74 

63 

53 

46 

40" 

35 

15 

421 

292 

214 

165 

130 

105 

87 

73 

62 

54 

47 

41 

16 

485 

338 

248 

189 

150 

121 

100 

84 

72 

62 

54 

47 

17 

555 

385 

284 

216 

171 

139 

115 

96 

82 

71 

62 

54 

18 

630 

437 

321 

246 

194 

157 

130 

109 

93 

80 

70 

61 

19 

667 

465 

341 

261 

206 

167 

138 

116 

99 

85 

74 

65 

20 

748 

521 

382 

293 

231 

187 

155 

130 

111 

95 

83 

73 

22 

924 

644 

472 

361 

285 

231 

191 

161 

137 

118 

103 

90 

24 

1119 

780 

571 

437 

345 

280 

231 

194 

166 

143 

125 

110 

26 

1330 

927 

680 

520 

410 

332 

275 

230 

197 

170 

148 

130 

28 

1560 

1083 

797 

610 

481 

390 

322 

271 

231 

199 

174 

153 

30 

1810 

1260 

925 

708 

558 

454 

374 

314 

268 

231 

202 

177 

36 

2586 

1808 

1322 

1010 

800 

648 

532 

450 

384 

331 

288 

254 

42 

3600 

2516 

1840 

1410 

1114 

903 

745 

626 

534 

460 

401 

353 

48 

4782 

3340 

2442 

1869 

1475 

1192 

988 

830 

708 

610 

532 

468 

Proportions,  1:6;  steel  reinforcement,  0.4  per  cent;  K=74;  £=3,000,000; 
h  -  depth  of  beam;  n  =  7.5;  /.-750;A  =20,000;  b=l;  d  =  depth  of  steel  from 
top  of  beam. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


131 


TABLE  XLVII  (Continued). — SAFE  LOADS  AND  STEEL  AREAS  FOR  BEAMS. 


Safe  load  in  Ibs.  per  linear  ft.  of  beam     • 

. 

g 

J3 

*j 

6 

1  inch  wide. 

Ifl 

3  . 

3-3 

P§ 

o  •+•* 

J 

Span  in  feet. 

1*1 

F 

4> 

Q 

•3.S.8 

*? 

1! 

o 
Q 

17 

18 

19 

20 

25 

30 

35 

Ibs. 

d 
ins. 

ins. 

sq. 
ins. 

M 

h 
ins. 

5.3 

4 

1 

.016 

1,392 

5 

6.3 

5. 

| 

.020 

2  175 

6 

7 

7.3 

6. 

i! 

.024 

3,132 

7 

10 

9 

78 

9 

8  4 

7 

i 

028 

4  262 

g 

12 

11 

9.6 

9 

9.4 

7.75 

1.25 

.031 

5J225 

9 

15 

14 

12.2 

11 

7 

....... 

10.5 

8.75 

.25 

.035 

6,661 

10 

19 

17 

15.2 

14 

10 

4  5 

11.5 

9.75 

.25 

.039 

8,270 

11 

23 

21 

18.5 

17 

11 

7 

5.4 

12.6 

10.75 

.25 

.043 

10,054 

12 

26 

23 

21.2 

19 

12 

8 

6.2 

13.7 

11.5 

.5 

.046 

11,506 

13 

31 

28 

25 

23 

14 

10 

7.3 

14.7 

12.5 

.5 

.05 

13,594 

14 

36 

32 

29 

26 

17 

12 

8.6 

15.8 

13.5 

.5 

.054 

15,856 

15 

42 

37 

33.6 

30 

19 

13 

9.9 

16.8 

14.5 

.5 

.058 

18  ,292 

16 

48 

43 

38.4 

35 

22 

15 

11.3 

17.9 

15.5 

.5 

.062 

20,903 

17 

54 

48 

43.5 

39 

25 

17 

12.8 

18.9 

16.5 

.5 

.066 

23,686 

18 

58 

51 

46.2 

42 

27 

19 

13.6 

20.0 

17 

.068 

25,143 

19 

65 

57 

51.9 

47 

30 

20.8 

15.2 

21.0 

18 

2 

.072 

28  ,188 

20 

80 

71 

64 

58 

37 

25.7 

18.8 

23.1 

20 

2 

.080 

34,800 

22 

97 

86 

77.5 

70 

45 

31.1 

22.8 

25.2 

22 

2 

.088 

42  ,108 

24 

115 

100 

92.1 

83 

53 

37 

27 

27.3 

24 

2 

.096 

50,012 

26 

135 

120 

108 

98 

62 

43.5 

31.8 

29.4 

26 

2 

.104 

55,712 

28 

157 

140 

125 

114 

72 

50.4 

37 

31.5 

28 

2 

.112 

68,208 

30 

224 

200 

180 

163 

103 

72.2 

52.8 

37.8 

33.5 

2.5 

.134 

106,357 

36 

312 

278 

250 

226 

144 

100 

73.4 

44.1 

39.5 

2.5 

.158 

135,742 

42 

414 

368 

331 

300 

191 

133 

97.2 

50.4 

45.5 

2.5 

.182 

180,112 

48 

M 


a;/3  X  12 


132 


REINFORCED    CONCRETE. 


TABLE  XLVIII. — SAFE  LOADS  AND  STEEL  AREAS  FOR  BEAMS. 


a 

i 

Saf 

2  load 

in  Ibs 

>.  per 

linear 

ft.  of 

beam 

1  inc 

i  wide 

«* 

o 

"o. 

S 

pan  in 

feet. 

* 

ins. 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

5 

32 

22 

16 

12 

10 

8 

g 

49 

34 

25 

19 

15 

12 

10 

9 

7 

71 

50 

36 

28 

22 

18 

15 

12 

10 

9 

8 

8 

97 

67 

49 

38 

30 

24 

20 

17 

14 

12 

11 

'"9" 

9 

119 

82 

61 

46 

37 

30 

25 

21 

17 

15 

13 

11 

10 

151 

105 

77 

59 

42 

38 

31 

26 

22 

19 

17 

15 

11 

188  • 

131 

97 

73 

58 

47 

39 

33 

28 

24 

21 

18 

12 

228 

158 

117 

89 

70 

56 

47 

40 

34 

29 

25 

22 

13 

262 

181 

134 

102 

80 

65 

54 

42 

39 

33 

29 

25 

14 

309 

214 

158 

120 

95 

77 

64 

53 

45 

39 

34 

23 

15 

360 

250 

184 

140 

111 

90 

75 

62 

53 

46 

40 

35 

16 

415 

288 

212 

162 

128 

103 

86 

72 

61 

53 

46 

40 

17 

475 

331 

243 

185 

146 

119 

99 

82 

70 

60 

53 

43 

18 

542 

378 

275 

216 

167 

135 

112 

94 

80 

69 

60 

52 

19 

573 

396 

291 

222 

176 

143 

116 

99 

84 

73 

63 

55 

20 

642 

445 

327 

250 

198 

160 

133 

111 

94 

81 

71 

62 

22 

792 

550 

404 

308 

244 

197 

164 

137 

117 

101 

88 

77 

24 

956 

665 

489 

372 

295 

248 

198 

166 

142 

124 

106 

93 

26 

1138 

793 

582 

443 

352 

284 

236 

197 

168 

145 

127 

111 

28 

1336 

925 

683 

520 

412 

333 

276 

232 

197 

170 

148 

130 

30 

1550 

1078 

792 

605 

478 

386 

320 

269 

229 

197 

172 

151 

36 

2220 

1540 

1134 

865 

685 

553 

459 

385 

328 

282 

246 

217 

42 

3085 

2140 

1576 

1204 

952 

770 

638 

535 

455 

393 

344 

299 

48 

4090 

2838 

2090 

1595 

1264 

1020 

845 

710 

605 

521 

455 

396 

Proportions,  1:6;  steel  reinforcement,  0.6  per  cent;  K=87;  E=  3,000,000; 
/t  =  depth  of  beam;  n=10;  /«-=750;/t  =  16,000;  &=•!;  d=depth  of  steel  from 
top  of  beam. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


133 


TABLE  XLVIII.  (Continued). — SAFE  LOADS  AND  STEEL  AREAS  FOR  BEAMS. 


Safe  load  in  Ibs.  per  linear  ft.  of  beam 

fl. 

1 

fc 

£ 

*"  a> 

B 

1  inch  wide. 

S-S* 

to 

"<u 

|ie 

C    M 

1 

^'pf  C 

o 

•Q'a5 

°"S) 

*°./i 

H" 

3:5*1 

e| 

o 
.d 

Span  in  feet. 

g-a 

"a 
Q 

V 

Q 

V 

02*0 

I 

d 

sq. 

h 

17 

18 

19 

20 

25 

30 

35 

Ibs. 

ins. 

ins. 

ins. 

M 

ins. 

5.3 

4 

1 

.024 

1  ,184 

5 

6.3 

5 

1 

030 

1J850 

6 

7  4 

6 

1 

.036 

2,664 

7 

8 

7 

8.4 

7 

1 

042 

3^626 

8 

10 

9 

8 

9.4 

7.75 

1.25 

.0465 

4,445 

g 

13 

12 

10 

9 

6 

10.5 

8  75 

1  25 

0525 

5,666 

10 

16 

14 

13 

12 

7 

11.6 

9^75 

L25 

!0585 

11 

20 

18 

16 

14 

9 

'"G" 

12.7 

10.75 

1.25 

.0645 

8  ,551 

12 

22 

20 

18 

16 

10 

7 

13.7 

11.5 

1.5 

.069 

9,787 

13 

27 

24 

21 

19 

13 

9 

14.7 

12.5 

1.5 

.075 

11  ,563 

14 

31 

28 

25 

23 

14 

10 

7 

15.8 

13.5 

1.5 

.081 

13,486 

15 

36 

32 

29 

26 

16 

11 

8 

16.8 

14.5 

1.5 

.087 

15,558 

16 

41 

37 

33 

30 

19 

13 

10 

17.9 

15.5 

1.5 

.093 

17  ,778 

17 

47 

41 

37 

34 

21 

15 

11 

19.0 

16.5 

1.5 

.099 

20.146 

18 

49 

44 

40 

36 

23 

16 

12 

19.9 

17 

2 

.102 

21,386 

19 

55 

49 

44 

40 

26 

18 

13 

21.1 

18 

2 

.108 

23  ,976 

20 

68 

61 

55 

50 

32 

22 

16 

23.2 

20 

2 

.120 

29,600 

22 

82 

74 

66 

60 

38 

27 

20 

25.3 

22 

2 

.132 

35,816 

24 

98 

88 

79 

71 

45 

32 

23 

27.4 

24 

2 

.144 

42  ,624 

26 

115 

103 

92 

84 

53 

37 

27 

29.5 

26 

2 

.156 

50,024 

28 

136 

120 

107 

97 

62 

43 

32 

31.6 

28 

2 

.168 

58,016 

30 

191 

172 

154 

139 

89 

62 

45 

38.0 

33.5 

2.5 

.201 

83  ,079 

36 

265 

249 

214 

194 

123 

86 

63 

43.3 

39.5 

2.5 

.237 

115,458 

42 

352 

317 

284 

258 

163 

114 

84 

50.6 

45.5 

2.5 

V273 

153  ,198 

48 

wl*  X  12 


134 


REINFORCED    CONCRETE. 


TABLE  XLIX — SAFE  LOADS  AND  STEEL  AREAS  FOR  BEAMS. 


1 

Saf 

2  load 

in  Ibs 

.  per 

linear 

ft.  of 

beam 

1  incl 

a  wide 

g 

s 

pan  in 

feet. 

h 

ins. 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

5 

55 

38 

28 

21 

16 

14 

11 

10 

6 

85 

59 

44 

34 

26 

21 

19 

15 

13 

11 

7 

123 

85 

63 

48 

38 

31 

25 

21 

19 

16 

14 

13 

8 

168 

116 

85 

65 

51 

41 

35 

29 

25 

21 

19 

16 

9 

205 

143 

105 

80 

64 

51 

43 

35 

30 

26 

24 

20 

10 

261 

181 

133 

103 

80 

65 

54 

45 

39 

34 

29 

25 

11 

324 

225 

165 

126 

100 

81 

68 

56 

48 

41 

36 

31 

12 

394 

274 

201 

154 

121 

99 

81 

69 

59 

50 

44 

39 

13 

450 

313 

230 

176 

139 

113 

93 

79 

66 

58 

50 

44 

14 

533 

370 

271 

208 

164 

133 

110 

93 

79 

68 

59 

53 

15 

621 

431 

316 

243 

191 

155 

129 

108 

91 

79 

69 

60 

16 

716 

498 

365 

280 

221 

179 

148 

124 

106 

91 

80 

70 

17 

819 

569 

418 

320 

253 

205 

169 

143 

121 

105 

91 

80 

18 

928 

644 

474 

363 

286 

231 

191 

161 

138 

119 

103 

90 

19 

985 

684 

503 

385 

304 

246 

204 

171 

145 

125 

110 

96 

20 

766 

564 

431 

340 

276 

228 

191 

164 

141 

123 

108 

22 

946 

695 

533 

420 

341 

281 

236 

201 

174 

151 

133 

24 

841 

644 

509 

413 

340 

286 

244 

210 

184 

161 

26 

766 

605 

490 

405 

340 

290 

250 

218 

191 

28 

900 

711 

576 

476 

400 

340 

294 

256 

225 

30 

825 

668 

551 

464 

395 

341 

296 

261 

36 

956 

790 

664 

565 

488 

425 

375 

42 

923 

786 

678 

590 

519 

48 

900 

784 

689 

Proportions,  1:6;  steel  reinforcement,  0.8  per  cent;  K=  102.2;  £=3,000,000; 
fc  =  depth  of  beam;  »=10;  /e=700;/.  =  14,000;  6  —  1;  d  =  depth  of  steel  from 
top  of  beam. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


135 


TABLE  XLIX.  (Continued). — SAFE  LOADS  AND  STEEL  AREAS  FOR  BEAMS. 


Safe  load  in  Ibs.  per  linear  ft.  of  beam 
1  inch  wide. 

fi 

li 

Depth  below 
steel.  | 

cat/   • 

I 

gs 

co'o 

Depth  of  beam,  j 

Span  in  ft. 

17 

18 

19 

20 

25 

30 

35 

Ibs. 

d 
ins. 

ins. 

sq. 
ins. 

M 

h 

ins. 

5.3 
6.3 
7.4 
8.5 
9.5 

10.6 
11.6 
12.7 
13.8 
14.8 

15.9 
16.9 
18.0 
19.1 
20.1 

21.2 
23.3 
25.4 
27.6 
29.7 

31.8 
38.1 
44.5 
50.9 

4. 
5. 
6. 
7. 
7.75 

8.75 
9.75 
10.75 
11.5 
12.5 

13.5 
14.5 
15.5 
16.5 
17. 

18. 
20. 
22. 
24. 
26. 

28. 
33.5 
39.5 
45.5 

1. 
1. 
1. 

!25 
.25 

:  .25 
:  .25 

.5 
.5 

.5 
.5 
.5 
.5 

2. 

2. 
2. 
2. 
2. 
2. 

2. 
2.5 
2.5 
2.5 

.032 
.040 
.048 
.056 
.062 

.070 
.078 
.086 
.092 
.10 

.108 
.116 
.124 
.132 
.136 

.144 
.160 
.176 
.192 
.208 

!268 
.316 
.364 

1,635 
2,555 
3,679 
5,008 
6,138 

7,825 
9,715 
11  ,811 
13  ,516 
15,969 

18  ,626 
21  ,487 
24,543 
27  ,824 
29,536 

33,113 
40  ,880 
49  ,465 
58,867 
69,087 

80,125 
114  ,694 
159  ,458 
211  ,579 

5 

6 
7 
8 
9 

10 

12 
13 
14 

15 
16 
17 
18 
19 

20 
22 
24 

28 

30 

36 
42 
48 

15 

18 

23 

28 
34 
39 
46 

54 
63 
71 

80 
85 

95 
118 
143 
170 
199 

231 
330 
460 
610 

20 
25 
30 
35 
41 

48 
55 
64 
71 
76 

85 
105 
128 
151 
178 

206 
295 
410 
544 

18 
23 
28 
31 
36 

43 
50 
56 
64 
69 

76 
94 
113 
136 
160 

185 

265 
368 
489 

16 
20 
25 
29 
34 

39 
45 

51 

58 
61 

69 
85 
103 
123 
144 

166 
239 
333 
441 

25 
29 
33 
38 
39 

44 
55 

66 
79 
93 

106 
153 
213 
275 

26 

28 

31 
38 
46 
55 
64 

74 
106 
148 
196 

"28" 
34 
40 

48 

55 
78 
109 
144 

M 


136 


REINFORCED    CONCRETE. 


TABLE  L. — SAFE  LOAD  PER  SQUARE  FOOT  AND  STEEL  AREA 
FOR  SLABS,  CONTINUOUS  AT  ENDS  ONLY. 


Thickness  | 

Safe  load  per  sq.  ft.,  including  wt.  of  slab. 

Span  in  feet. 

h  ins. 

4|         5|         6|         7        |       8      |        9      |      10 

1      H 

=  0.004;    /c=460. 


3 
3} 

t1 

6 

7 
8 

160 
239 
334 
387 
506 
791 
1138 
1549 

102 
153 
214 
248 
324 
506 
729 
992 

71 
106 
148 
172 
225 
351 
506 
689 

52 

78 
109 
126 
165 
258 
372 
506 

40 
60 
83 
97 
127 
198 
285 
387 

32 
47 
66 
77 
100 
156 
225 
306 

26 
38 
53 

62 
81 
126 

182 
248 

21 
32 
44 
51 
67 
105 
151 
205 

0.006; 


580. 


3 

235 

150 

104 

77 

59 

46 

38 

31 

3i 

351 

225 

156 

115 

88 

69 

56 

46 

4 

491 

314 

218 

160 

123 

97 

78 

65 

4* 

569 

364 

253 

186 

142 

112 

91 

75 

5 

743 

476 

330 

243 

186 

147 

119 

99 

6 

1161 

743 

516 

379 

290 

229 

186 

154 

7 

1672 

1070 

743 

546 

418 

330 

268 

221 

8 

2276 

1456 

1011 

743 

569 

449 

384 

301 

=  0.008;    /e=680. 


3 
3i 

1' 

6 
7 
8 

309 
461 
645 
747 
976 
1525 
2196 
2989 

198 
299 
412 
478 
625 
976 
1405 
1913 

137 
205 

286 
332 
434 
677 
976 
1328 

101 
151 
210 
244 
319 
498 
717 
976 

77 
115 
161 
187 
244 
381 
549 
747 

61 
91 
127 
148 
193 
301 
434 
590 

49 
74 
103 
120 
156 
244 
351 
478 

41 
61 

85 
98 
129 
202 
290 
395 

•  =  0.010:    /e=700. 


3 
? 

9 

6 
7 

8 

381 
569 
795 
922 
1204 
1881 
2709 
3687 

244 
364 
509 
590 
771 
1204 
1734 
2360 

169 
253 
353 
410 
535 
836 
1204 
1639 

124 
186 
260 
303 
393 
614 
884 
1204 

95 
142 
198 
230 
301 
470 
677 
922 

75 
112 

157 
182 
238 
372 
535 
728 

61 
91 
127 
147 
193 
301 
433 
590 

50 

75 
105 
122 
160 
248 
359 
488 

£  =  0.012;  /,=  700. 

3 
3} 

r 

8 

.   421 
629 
878 
1018 
1330 
2078 
2993 
4073 

269 
402 
562 
652 
851 
1330 
1915 
2607 

187 
279 
390 
453 
591 
924 
1330 
1810 

137 
205 
287 
332 
434 
678 
977 
1330 

105 
157 
219 
255 
333 
520 
748 
1018 

83 
124 
174 
201 
263 
410 
591 
805 

67 
101 
140 
163 
213 
332 
479 
652 

56 
83 
113 
135 
176 
275 
396 
538 

BUILDING  DESIGN  AND  CONSTRUCTION. 


137 


TABLE  L.  (Continued). — SAFE  LOAD  PER  SQUARE  FOOT  AND  STEEL  AREA 
FOR  SLABS.  CONTINUOUS  AT  ENDS  ONLY. 


Safe  load  per  sq.  ft.,  including 
wt.  of  slab. 

ft 

£ 

g| 

2  . 
3l 

r 

i 

jD 

"3   . 

.o-a 

.s  « 
aw 

V 

Q 

s|. 

Ss-S 

Safe  moment 
of  resistance. 

Thickness. 

Span  in  feet. 

l£ 

M« 

12      |      13      |      14      |      15 

Ibs.     |  d  ins.  |     ins.     |  sq.  ins. 

in.  Ibs.  |  h  ins. 

=  0.004;    /c=460. 


18 
27 
37 
43 
56 
88 
121 
172 

15 
23 
32 
37 
48 
75 
108 
147 

13 
19 
27 
32 
41 
65 
93 
122 

11 
17 
24 
28 
36 
56 
81 
110 

37.8 
44.2 
50.4 
56.7 
63.0 
75.6 
88.2 
100.8 

21 
3i 
3* 
4 
5 
6 
7 

1 
1 
1 
1 
1 

.108 
.132 
.156 
.168 
.192 
.240 
.288 
.336 

3,070 
4,590 
6,410 
7,440 
9,720 
15  ,180 
21,860 
29,750 

3 

? 

i» 

6 
7 
8 

=  0.006;    /e=580. 


26 

22 

19 

17 

37.9 

2i 

.162 

4  ,510 

3 

39 

33 

29 

25 

44.3 

2f 

.192 

6,740 

3} 

55 

46 

40 

35 

50.5 

31 

.234 

9,420 

4 

63 

54 

46 

40 

56.8 

3i 

1 

.252 

10  ,920 

4} 

83 

70 

61 

53 

63.2 

4 

1 

.288 

14  ,270 

5 

129 

110 

95 

83 

75.8 

5 

.360 

22,290 

6 

186 

158 

136 

119 

88.6 

6 

1 

.432 

32,100 

7 

253 

215 

186 

162 

101.2 

7 

1 

.504 

43,690 

8 

=  0.008;    /c=680. 


34 
51 

72 
83 
108 
170 
244 
332 

29 
44 

61 
71 
92 
144 

208 
283 

25 
38 
53 
61 
80 
125 
179 
244 

22 
33 
46 
53 
69 
108 
156 
213 

38.0 
44.4 
50.7 
57.0 
63.4 
76.1 
88.9 
101.6 

4 
5 
6 
7 

.216 
.264 
.312 
.336 
.384 
.480 
.576 
.672 

5,930 
8,860 
12  ,370 
14,350 
18  ,740 
29,280 
42,160 
57.390 

3 

? 

45* 

6 

7 
8 

P-- 

=  0.010; 

/«=  700 

42 
63 
88 
102 
134 
209 
301 
410 

36 
54 
75 
87 
114 
178 
256 
349 

31 

46 
65 
75 
98 
154 
221 
301 

27 
40 
57 
66 
86 
134 
193 
262 

38.1 
44.5 
50.9 
57.2 
63.6 
76.4 
89.2 
102.0 

21 
31 
3i 
4 
5 
6 
7 

.270 
.330 
.390 
.420 
.480 
.600 
.720 
.840 

7,320 
10,930 
15,260 
17,700 
23,120 
36  ,120 
52  ,020 
70,800 

3 

f 

4* 
5 

6 

7 
8 

=  0.012;    /e=700. 


47 

40 

34 

30 

38.3 

21 

.324 

8,080 

3 

70 

98 

60 
83 

51 

72 

45 
62 

44.6 
51.1 

If 

.396 
.468 

12  ,070 
16,860 

113 

96 

83 

72 

57.3 

3* 

1 

.504 

19,550 

41 

148 

126 

109 

95 

63.9 

4 

1 

.576 

25,540 

5 

231 

197 

170 

148 

76.7 

5 

1 

.720 

39,900 

6 

333 

283 

244 

213 

89.5 

6 

1 

.864 

57,460 

7 

453 

386 

332 

290 

102.4 

7 

1 

1.008 

78.200 

8 

;  =  15;   M  - 


X    12 
10 


-  Kbd*. 


138 


REINFORCED    CONCRETE. 


TABLE   LI. — SAFE    LOAD    PER   SQUARE    FOOT    AND    STEEL   AREA 
FOR  SLABS,  EITHER  CONTINUOUS  OR  FIXED  AT  THE  FOUR  EDGES. 


jl 

Thickness. 

Safe  load  per  sq.  ft., 

including  wt. 

of  slab. 

Span 

in  feet. 

/tins. 

4        |         5        |          6        | 

7        1 

8 

|        9      |      10 

1      11 

=  0.004;    /«=460. 


3 

320 

205 

142 

105 

80 

63 

51 

42 

3} 

478 

306 

213 

156 

120 

94 

76 

63 

4 

668 

428 

297 

218 

167 

132 

107 

88 

4} 

775 

496 

344 

253 

194 

153 

124 

102 

5 

1012 

648 

450 

330 

253 

200 

162 

134 

6 

1581 

1012 

703 

516 

395 

312 

253 

209 

7 

2277 

1457 

1012 

744 

569 

450 

364 

301 

8 

3099 

1984 

1377 

1012 

775 

612 

496 

410 

0.006;   /e=580. 


3 

470 

301 

209 

154 

118 

93 

75 

62 

31 

702 

450 

312 

229 

176 

139 

112 

93 

4 

981 

628 

436 

320 

245 

194 

157 

130 

41 

1137 

728 

506 

371 

284 

225 

182 

150 

5 

1486 

951 

660 

485 

372 

294 

238 

197 

6 

.  2322 

1486 

1032 

758 

580 

459 

371 

307 

7 

3343 

2140 

1486 

1092 

836 

660 

535 

442 

8 

4551 

2913 

2023 

14S6 

1138 

899 

728 

602 

0.008:    /e=680. 


I 

? 

6 
7 
8 

617 
923 
1288 
1494 
1952 
3050 
4392 
5978 

396 
590 
825 
956 
1249 
1952 
2811 
3826 

274 
410 
573 
664 
868 
1355 
1952 
2657 

202 
301 
421 
488 
637 
996 
1434 
1952 

154 
231 
322 
374 
488 
762 
1098 
1495 

122 

182 
254 
295 
386 
602 
867 
1181 

99 
148 
206 
239 
312 
489 
703 
956 

82 
122 
170 
198 
258 
403 
581 
790 

=  0.010;    /«=700. 


3 
31 

? 

6 
7 
8 

762 
1138 
1590 
1844 
2408 
3763 
5419 
7375 

488 
729 
1018 
1180 
1541 
2408 
3468 
4720 

339 
506 
707 
819 
1070 
1672 
2408 
3278 

249 
372 
519 
602 
786 
1229 
1769 
2408 

190 
285 
397 
461 
602 
941 
1355 
1844 

151 
225 
314 
364 
476 
743 
1070 
1457 

122 
182 
254 
295 
385 
602 
867 
1180 

101 
151 
210 
244 
318 
498 
717 
975 

=  0.012;    /e=700. 


3 

842 

539 

374 

275 

210 

166 

135 

111 

1257 

805 

559 

411 

314 

248 

201 

166 

4 

1756 

1124 

780 

573 

439 

347 

281 

232 

41 

2037 

1303 

905 

665 

509 

402 

326 

269 

5 

2660 

1702 

1182 

869 

665 

525 

426 

352 

6 

4156 

2660 

1847 

1357 

1039 

821 

665 

550 

7 

5985 

3830 

2660 

1954 

1496 

1182 

958 

791 

8 

8146 

5214 

3620 

2660 

2037 

1609 

1303 

1077 

IK.    K/r        u//8   X   12         „,  ,3 
n— 15:  M  «» TTT =  KM3. 


BUILDING  DESIGN  AND  CONSTRUCTION.         139 


TABLE  LI.  (Continued). — SAFE  LOAD  PER  SQUARE  FOOT  AND  STEEL  AREA 
FOR  SLABS,  EITHER  CONTINUOUS  OR  FIXED  AT  THE  FOUR  EDGES. 


Safe  load  per  sq.  ft.,  including 
wt.  of  slab. 

*§"*•' 

If 

Jj* 

a 

11 

(D  W 

Q 

£ 

o 

I* 

5-2 

a"3 

| 

Zfa 

rt  >  d 
iW 

*F 

Safe  moment 
of  resistance. 

Thickness. 

Span  in  feet. 

13 


14       |      15 


Ibs.     |  dins.  |     ins.     |  sq.ins.  |  in.lbs.  |  fcins. 


=  0.004;   /c=460. 


36 

30 

26 

23 

37.8 

2i 

.108 

3,070 

3 

53 

45 

39 

34 

44.2 

2f 

.132 

4,590 

31 

74 

63 

54 

48 

50.4 

31 

.156 

6,410 

4 

86 

73 

63 

55 

56.7 

31 

1 

.168 

7,440 

112 

96 

83 

72 

63.0 

4 

1 

.192 

9,720 

5 

176 

150 

129 

112 

75.6 

5 

1 

.240 

15,180 

6 

253 

216 

186 

162 

88.2 

6 

1 

.288 

21,860 

7 

344 

293 

253 

220 

100.8 

7 

1 

.336 

29,750 

8 

p  =  0.006;    /c=580. 


52 
78 
109 
126 
165 
258 
372 
506 

45 
66 
93 
108 
141 
220 
316 
431 

38 
57 
80 
93 
121 
190 
273 
371 

33 
50 
70 

81 
106 

165 
238 
324 

37.9 
44.3 
50.5 

56.8 
63.2 
75.8 
88.6 
101.2 

5 

5 

,1 
! 

.162 
.192 
.234 
.252 
.288 
.360 
.432 
.504 

4,510 
6,740 
9,420 
10  ,920 
14  ,270 
22,290 
32,100 
43  ,690 

3 
3* 

!J 

6 
7 
8 

=  0.008;    /8=680. 


69 
103 
143 
166 
217 
339 
488 
664 

58 
87 
122 
141 
185 
288 
416 
566 

50 
75 
105 
122 
159 
249 
359 
488 

44 
66 
92 
106 
139 
217 
312 
425 

38.0 
44.4 
50.7 
57.0 
63  4 
76.1 
88.9 
101.6 

4 
5 
6 

7 

' 

.216 
.264 
.312 
.336 
.384 
.480 
.576 
.672 

5,930 
8,860 
12  ,370 
14,350 
18  ,740 
29  ,280 
42,160 
57  ,390 

3 

3} 

4* 
5 
6 

7 
8 

=  0.010;   /c=700. 


85 
126 
177 
205 
268 
418 
602 
820 

72 
107 
151 
175 
228 
356 
513 
698 

62 
93 
130 
151 
196 
307 
442 
602 

54 
81 
113 
131 
171 
268 
385 
524 

38.1 
44  5 
50.9 
57.2 
63.6 
76.4 
89.2 
102.0 

2f 

5 

6 
7 

1 
1 
1 
1 

1 

.270 
.330 
.390 
.420 
.480 
.600 
.720 
.840 

7,320 
10,930 
15,260 
17,700 
23  ,120 
36  ,120 
52  ,020 
70,800 

3 
7 

\      £  =  0.012;  /«=700. 

94 
140 
195 
226 
295 
462 
665 
905 

80 
119 
166 
193 
252 
393 
565 
771 

69 
103 
143 
166 
217 
339 
489 
665 

60 
90 
125 
145 
190 
296 
426 
580 

38.3 
44.6 
51.1 
57.3 
63.9 
76.7 
89.5 
102.4 

4 
5 
6 

7 

' 

.324 
.396 
.468 
.504 
.576 
.720 
.864 
1.008 

8,080 
12  ,070 
16,860 
19,550 
25,540 
39,900 
57,460 
78,200 

3 
7 

US-    M 
n=15;  M  = 


X    12 


140  REINFORCED    CONCRETE. 

The  following  tables  are  taken  by  permission — from  Lin- 
dau's  "Designing  Methods" — and  are  based  upon  ultimate 
bending  moments  of 

3  LL  -f  2  DL  or 

4  LL  +  2  DL 

as  the  case  may  be. 

The  following  formulas  are  used  in  preparing  the  tables: 

FORMULAS     GIVING    THE    ULTIMATE    STRENGTH 
OF  BEAMS— A   TAKEN   AS  50,000  LBS. 

Class  No.  1,  Average  Rock  Concrete. — This  class  is  meant 
tc  include  all  concretes  having  a  compressive  strength  of 
2000  Ibs.  per  square  inch;  fc  then  =  2000  and  taking  EK 
=  2,600,000  we  get  for  the  ultimate  resisting  moment: 

MQ  =  370  bd^  for  A*  =  0.0085  bd (1) 

Class  No.  2,  Good  Rock  Concrete.— By  using  a  1  :2:4 
mix  and  good  rock  or  gravel  we  get  a  concrete  of  much 
greater  compressive  strength,  but  with  a  higher  modulus  of 
elasticity.  For  such  a  concrete  we  may  assume  Ec  =  2,800,000 
and  fc  —  2700,  and  we  get: 

M0  =  570  bcl^  for  As  =  0.013  bd (2) 

Class  No.  3,  Cinder  Concrete. — For  a  1  :  2  :  5  mix  of 
cinder  concrete  we  may  assume  £c  =  750,000  and  f< 
~  750;  then  we  have: 

Mo  =  207  bd*  for  As  =  0.0047  bd....  .(3) 


BUILDING  DESIGN  AND  CONSTRUCTION.         141 


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142 


REINFORCED    CONCRETE. 


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BUILDING  DESIGN  AND  CONSTRUCTION. 


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single  panels  or  slabs  free  at  both  ends,  use  of  abo 


144  REINFORCED    CONCRETE 

COLUMNS. 

There  is  a  scarcity  of  comparable  experimental  data  on  the 
strength  of  reinforced  concrete  columns  from  which  reliable 
formulae  might  be  derived.  Experiments  to  determine  the 
compressive  strength  of  concrete,  even  when  made  on  care- 
fully-prepared test  specimens,  give  widely  divergent  results, 
and  conservative  values  for  the  allowed  stresses  should  be 
used  in  designing.  It  is,  of  course,  desirable  in  column  de- 
sign to  use  high-unit  stresses,  in  order  that  the  column  may 
be  comparatively  small. 

It  is  desirable  and  necessary  that  there  be  some  longi- 
tudinal reinforcement  in  a  concrete  column,  since,  owing  to 
the  monolithic  character  of  reinforced  concrete  buildings, 
more  or  less  bending  moment  will  be  put  into  the  columns; 
this  applies  particularly  to  the  end  or  wall  columns.  When 
the  bending  moment  can  be  figured,  as  is  the  case  when  the 
eccentricity  of  loading  is  known,  or  when  the  design  contem- 
plates the  resistance  of  wind  stresses  through  knee-brace 
action  the  stresses  due  to  both  the  direct  load  and  the  bend- 
ing moment  must  be  taken  into  consideration. 

In  the  discussion  following,  the  columns  will  be  considered 
as  axially  loaded. 

A  simple  and  reliable  method  of  increasing  the  strength 
of  a  given  concrete  is  by  the  use  of  a  greater  amount  of 
cement.  The  use  of  a  special  mix  for  the  columns  only  of  a 
reinforced  concrete  structure,  is  attended  with  considerable 
practical  difficulty,  and  the  practice  is  not  to  be  recommended 
unless  the  work  is  inspected  with  the  utmost  thoroughness. 
It  is  also  essential  that  the  column  shaft  be  carried  up 
through  the  beam  and  girder  levels,  using  the  special  mix, 
and  this  presents  many  difficulties. 

The  following  table  gives  the  compressive  strength  of 
broken  stone  concrete  from  Kimball's  tests,  made  at  Water- 
town  Arsenal,  in  1899,  on  12-in.  cubes,  and  while  the  re- 
sults may  not  be  good  averages  for  the  strength  generally, 
yet  they  show  the  comparative  strength  of  the  various  mix- 
tures at  different  ages: 


BUILDING  DESIGN  AND  CONSTRUCTION.         145 


TABLE  LI-D. — CRUSHING  STRENGTH  IN  POUNDS  PER  SQUARE  INCH. 


Mixture. 

7  Days. 

1  Month. 

3  Months. 

6  Months. 

1:1         3 
1:2         4 
1  :2y2      5 
1  :3          6 
1  :  3H      7 
1  :4         8 
1:5        10 
1:6        12 

1,600 
1,525 
1,300 
1,230 
1,100 
1,000 
800 
600 

2,750 
2,460 
2,225 
2,060 
1,875 
1,700 
1,350 
1,000 

3,360 
2,944 
2,670 
2,440 
2,210 
1,980 
1,520 
1,060 

4,300 
3,900 
3,400 
3,100 
2,800 
2,500 
1,900 
1,300 

The  following  table  gives  the  crushing  strength  of  plain 
concrete  columns,  and  has  been  arranged  from  the  results  re- 
ported by  Prof.  Talbot,  in  Bulletin  No.  10,  of  the  University 
of  Illinois  Experiment  Station.  These  columns  were  made  of 
a  1:2:4  mix  of  limestone  concrete,  and  should  represent 
average  conditions  met  with  in  practice.  It  is  the  purpose 
of  the  table  to  show  what  strength  may  be  expected  of  such 
columns,  and  also  to  bring  out  the  wide  difference  between 
the  compressive  strength  of  the  concrete,  as  determined  from 
tests  on  cubes  and  cylinders  of  the  dimensions  noted. 

TABLE  LI-E. — COLUMN  TESTS — UNIVERSITY  OF  ILLINOIS  EXPERIMENT  STATION. 


Column 
Number. 

Size  and 
Length. 

Maximum 
Total 
Pounds. 

Loads  Carried 
Lbs.  per  Sq.  In. 
of  Gross  Area. 

Age  in 
Days. 

5 
8 
9 
13 
15 
18 

12'xl2*xl2'0" 
9*x  9"xl2'0" 
12*xl2"xl2'0* 
12*xl2"xl2'0" 
12"xl2"x  6'0" 
9'x  9'x  6'0* 

Averages.  

250,200 
162,000 
236,000 
254,000 
176,000 
90,300 

1,710 
2,004 
1,610 
1,709 
1,189 
1,079 

69 
64 
65 
61 
63 
65 

1,550 

65 

Above  columns,  limestone  concrete  1:2:3%  mix. 

Average  crushing  strength  of  columns — 1550,  Age  65  days. 

Average  crushing  strength  of  12-in.  cubes — 210C,  Age  64 
days. 

Average  crushing  strength  of  cylinders  8  ins.  in  diameter 
and  16  ins.  long — 1490,  Age  73  days. 

The  following  diagram  gives  the  average  unit  stress  in 
reinforced  concrete  columns  with  varying  percentages  of 
longitudinal  reinforcement  based  on  allowable  unit  stresses, 


146 


REINFORCED    CONCRETE. 


fc'm  plain  columns  of  500,  600  and  700  pounds  per  square  inch, 
the  ratio  of  the  moduli  being  taken  as  15.  (After  Lindau: 
"Designing  Methods".) 


Percen  taoe  of  Reinforqment  «=  q i 
Diaqram  Plotted  from  Formula 
P=fc  (Ac+l5As) 

Fig.   60-A. 


The  following  values  for  the  crushing  strength  of  columns, 
with  longitudinal  reinforcement  from  tests  on  full-sized 
specimens,  should  be  of  value  as  bases  of  comparison. 


Experimenter. 

Average 
Crushing  Strength 

.       P 

persq.  "1.  =  ^. 

Average 
Percentage  of 
Reinforcement. 

Mix  of 
Concrete. 

Age  in 
Days. 

Talbot 
Average  of  11  Tests  .  . 
Watertown  Arsenal 
Average  of  4  Tests.... 

1,746  pounds 
2,015  pounds 

1.39 
1.34 

1:2:4 
1  :2:4 

66 
104 

BUILDING  DESIGN  AND  CONSTRUCTION.         147 

Classification  of  Columns. — There  are  several  kinds  of  re- 
inforced concrete  columns  in  use  to  date: 

(1)  Rectangular  or  polygonal   columns,   reinforced  with 
straight  rods,  tied  together  at  intervals  with  plates,  rods  or 
bands. 

(2)  Hooped    columns    with   spiral    continuous    reinforce- 
ment encircling  the  column  at  close  intervals  and  containing 
additional  vertical  rods,  invented  by  Considere. 

(3)  Hooped    columns    with    annular    rings   of    round    or 
band  iron  also  kept  spaced  by  vertical  reinforcement,  as  in 
the  Cummings  system. 

(4)  Expanded   metal   hooped  columns,   where    expanded 
metal  lathing  incloses  and  restrains  the  concrete. 

(5)  Structural  steel  or  cast  iron  columns  filled  with  con- 
crete. 

Rectangular  or  Polygonal  Columns. — In  rectangular  or 
polygonal  columns  four  or  more  vertical  rods  are  tied  to- 
gether horizontally  by  wires  or  plates  placed  at  a  distance 
apart  very  nearly  the  maximum  horizontal  dimension  of  the 
column,  each  band  being  firmly  fastened  by  wire  or  other- 
wise to  the  vertical  rods.  This  construction  was  used  in 
the  Winton  Garage  in  Chicago,  designed  by  the  author  in 
1903.  At  the  bottom  of  the  columns  the  rods  rest  on  a 
24x24xJ/2-in.  steel  plate  bedded  in  the  concrete  footing.  The 
joints  occur  6  ins.  above  each  floor  level  and  are  made  with 
a  sleeve  of  gas  pipe,  into  which  the  ends  of  the  two  sections 
of  rods  are  wedged.  A  1-2-2  mixture  was  used  for  this  con- 
struction and  the  following  shows  the  method  of  calculation 
employed: 


148  REINFORCED    CONCRETE, 

Size  of  column  20  ins.  X  20  ins.  =  400  sq.  ins. 
Four  rods,  2&  ins.  in  diameter  =  5.1572  X  4  =  20.6288  sq.  ins. 
P  =  load  on  column. 

fc  =  safe  stress  on  concrete  in  Ibs.  per  sq.  in. 
Ac  =  area  of  concrete  in  sq.  ins. 

«  =  ratio  between  modulus  of  elasticity  of  steel  and  concrete. 
As  =  area  of  vertical  steel. 
A  =  total  net  area. 
P=fc  (Ac  +  nA8)  =  fcAc(l  +  (n  —  \}p) 

p  =  600  X  400  (1  +  (10  —  1)  2°4QQ88  =  351.360  Ibs. 

It  will  be  noticed  that./£  was  assumed  at  600  Ibs.  per  sq. 
in.  and  n  at  10. 

A  similar  construction  was  used  in  the  Ingalls  building 
in  Cincinnati,  16  stories  high,  and  here  the  wind  pressure 
was  taken  care  of  by  additional  twisted  rods  running  up  par- 
allel to  the  carrying  rods. 

For  factory  buildings  the  columns  carrying  traveling 
cranes  are  exposed  to  eccentric  loads  and  must  be  calculated 
accordingly.  Besides,  the  crane-carrying  brackets  must  be 
carefully  tied  to*  the  column.  A  good  construction  for  this 
purpose  is  that  employed  in  the  screen  house  of  Ontario 
Power  Co.  of  Niagara  Falls,  Ontario.  The  columns  are 
12x15  ins.  in  section  and  support  the  direct  load  of  heavy 
roof  beams  and  an  eccentric  load  from  a  20x60-in.  reinforced 
concrete  girder,  resting  upon  brackets  in  the  inner  side  of 
the.  columns.  The  column  reinforcement  consists  of  four 
rods  \l/4  ins.  in  diameter  fastened  together  by  ties  in  the 
usual  manner.  The  brackets  extend  15  ins.  from  the  col- 
umns to  which  they  are  fastened  and  are  12  ins.  wide.  Wall 
columns  of  this  style  are  usually  rectangular  or  tee  form, 
or  even  of  hollow  sections. 

Hooped  Columns. — Hooped  columns  to  be  effective  should 
have  the  hoops  in  circular  form,  either  as  a  helix  or  as  a  series 
of  annular  hoops,  such  as  is  used  in  the  Cummings,  Ameri- 
can or  Monolith  systems,  Figs,  26  to  29.  In  Tables  LIT  to  LVII 
the  requirements  of  New  York  City  and  Brooklyn  are  practically 
covered  and  the  tables  are  safe,  as  may  be  readily  seen  by  com- 
parisons with  ultimate  loads  according  to  the  empirical  formula 


BUILDING  DESIGN  AND  CONSTRUCTION.         149 

of  Considere  as  tabulated  in  Table  LVIII,  "Hooped  Columns, 
Considered  Formula." 

Where  the  load  to  be  carried  is  moderate,  so  that  longi- 
tudinal reinforcement  is  not  required  to  assist  in  carrying 
it,  a  very  efficient  form  of  hooping  can  be  made  by  rolling 
sheets  of  expanded  metal  into  cylinders,  causing  all  adjacent 
edges  to  overlap  so  as  to  interlock  the  meshes.  If  securely 
wired,  the  cylinder  thus  composed  of  a  right  and  a  left 
spiral  of  intersecting  strands,  will  act  not  only  as  a  hoop- 
ing, but  also  as  longitudinal  reinforcement  to  resist  flexure. 

Design  of  Hooped  Columns.  —  To  reduce  the  area  of  floor 
columns  and  accordingly  increase  available  floor  space  has 
been  one  of  the  most  important  problems  in  reinforced  con- 
crete building  construction.  Owing,  however,  to  the  unfin- 
ished state  of  actual  tests  and  the  uncertainty  of  the  value 
of  both  empirical  formulas  and  the  application  of  the  elastic 
theory  to  a  composite  body,  the  calculation  of  columns  both 
for  direct  and  eccentric  loads  is  quite  intricate,  and  we  will 
here  merely  give  such  methods  as  have  been  accepted  in  the 
principal  municipalities  in  the  United  States  with  tables 
showing  comparative  values  for  different  assumed  condi- 
tions. 

Tables  LII  to  LVII,  inclusive,  are  compiled  from  the  fol- 
lowing formula: 


(22) 


where  P  =  safe  load  in  Ibs. 

fc=  stress  in  concrete  per  sq.  inch  (500  Ibs.  or  750  Iba.) 

^8  f  , 

/»  =  ~j?~  fc  =  njc 

ft  =  tensile  stress  in  hoop 
Ac~  area  of  concrete  inside  hoop 
At  =  area  of  longitudinal  rods 
A  '•  =  area  of  hoops  per  unit  height  of  column 

r  =  radius  of  concrete  core  inside  of  hoop 

In  these  tables  medium  steel  is  assumed  where  /%=  16,000  Ibs. 
per  sq.  in. 


150  REINFORCED    CONCRETE. 

TABLE  LII. — HOOPED  COLUMNS;   rc=12;  y«=5CO. 
1-in.  Hooping  at  H  ins.  centers. 


0.5%. 

0.7%. 

Safe 

Load. 

Diameter 

Area  of 

Area  of 

Diameter 

Area  of 

Area  of 

of  ^Hooping 

Concrete 

Steel 

of  Hooping 

Concrete 

Steel 

in  ins. 

in  sq.  ins  . 

in  sq.  ins. 

in  ins. 

in  sq.  ins. 

in  sq.  ins. 

100,000 

12.78 

128 

.64 

12.72 

127 

.889 

150,000 

16.24 

206 

1.03 

16.12 

203 

1.42 

200,000 

19.24 

300 

1.50 

19.16 

287 

2.11 

250,000 

21.84 

374 

1.87 

21.72 

370 

2.54 

300,000 

24.04 

452 

2.26 

23.92 

449 

3.14 

350.000 

26.0 

530 

2.65 

25.92 

527 

3.68 

400.000 

28.0 

616 

3.08 

27.92 

611 

4.28 

450,000 

30.0 

706 

3.53 

29.72 

693 

4.84 

500,000 

31.84 

792 

3.96 

31.62 

784 

6.45 

550.000 

33.44 

876 

4.38 

33.32 

871 

6.02 

600,  000 

35.0 

960 

4.80 

34.92 

957 

6.70 

650.000 

36.64 

1050 

5.25 

36.32 

1035 

7.20 

700.000 

38.0 

1130 

5.65 

37.72 

1116 

7.81 

750.000 

39.6 

1232 

6.16 

39.12 

1200 

8.40 

800.000 

41.0 

1320 

6.60 

40.52 

1288 

9.00 

850,000 

42.3 

1406 

7.03 

41.90 

1379 

9.65 

900.000 

43.6 

1494 

7.47 

43.00 

1452 

10.20 

950,000 

44.9 

1584 

7.92 

44.50 

1555 

10.90 

1,000,000 

46.2 

1676 

8.37 

45.70 

1640 

11.50 

J-in.  Hooping  at  2  ins.  centers. 


100,000 

13.5 

143 

.72 

13.3 

139 

.97 

150,000 

17.0 

227 

1.13 

16.8 

222 

1.53 

200,000 

19.8 

308 

1.54 

19.6 

302 

2.12 

250,000 

22.4 

394 

1.97 

22.2 

387 

2.72 

300,000 

24.6 

475 

2.38 

24.2 

468 

3.35 

350.000 

26.8 

564 

2.84 

26.5 

552 

3.90 

400,000 

28.9 

656 

3.28 

28.6 

642 

4.50 

450  000 

30.7 

740 

3.70 

30  4 

725 

5.10 

500,000 

32.6 

834 

4.17 

32.2 

814 

5.70 

550,000 

34.3 

924 

4.62 

33.9 

903 

6.40 

600,000 

36.1 

1024 

5.12 

35.7 

1001 

7.00 

650,000 

37.5 

1104 

5.52 

37.0 

1057 

7.30 

700,000 

38.9 

1188 

5.94 

38.5 

1164 

8.15 

750,000 

40.3 

1276 

6.38 

39.8 

1244 

8.70 

800.000 

41.7 

1366 

6.83 

41.3 

1340 

9.35 

850,000 

43.0 

1452 

7.26 

42.6 

1425 

10.15 

900,000 

44.4 

1548 

7.74 

44.0 

1521 

10.60 

950.000 

45.0 

1633 

8.16 

45.2 

1604 

11.20 

1.000.000 

47.0 

1735 

,8.68 

46.4 

1691 

11.80 

500—1' 


BUILDING  DESIGN  AND  CONSTRUCTION. 


151 


TABLE  LIII. — HOOPED  COLUMNS;   n=12;  fc=  500. 


|-in.  Hooping  at  1J  ins.  centers. 


0.5%. 

0.7%. 

Safe 

Load. 

Diameter 

Area  of 

Area  of 

Diameter 

Area  of 

Area  of 

of  Hooping 

Concrete 

Steel 

of  Hooping 

Concrete 

Steel 

in  ins. 

in  sq.  ins. 

in  sq.  ins. 

in  ins. 

in  sq.  ins. 

in  sq.  ins. 

100,000 

10.2 

81.7 

.41 

10.2 

81.7 

.57 

150.000 

13  5 

143 

.71 

13.3 

139 

.98 

200,000 

16.2 

206 

1.03 

16.0 

201 

1.41 

250,000 

18.8 

278 

1.39 

18.6 

272 

1.90 

300,000 

21.0 

346 

1.73 

20.8 

340 

2.38 

350,000 

23.0 

415 

2.07 

22.6 

401 

2.81 

400,000 

25.0 

491 

2.45 

24.8 

483 

3.38 

450,000 

27.0 

572 

2.86 

26.6 

556 

3.90 

500,000 

28.8 

651 

3.26 

28.4 

633 

4.45 

550,000 

30.4 

726 

3.63 

30.0 

707 

4.95 

600,000 

32.0 

804 

4.02 

31.6 

784 

5.50 

650,000 

33.6 

887 

4.44 

33.0 

855 

•6.00 

700,000 

35.0 

962     . 

4.81 

34.6 

940 

6.60 

750,000 

36.4 

1040 

5.20 

35.8 

1007 

7.10 

800,000 

37.8 

1122 

5.61 

37.4 

1098 

7.60 

850,000 

39.2 

1207 

6.03 

38.6 

1170 

8.20 

900.000 

40.4 

1282 

6.41 

39.8 

1244 

8.70 

950,000 

41.8 

1372 

6.86 

41.2 

1333 

9.20 

1,000,000 

43.0 

1452 

7.26 

42.4 

1412 

9.90 

j-in.  Hooping  at  2  ins.  centers. 


100,000 

11.3 

100 

.50 

11.2 

98 

.69 

150,000 

14.7 

170 

.85 

14.5 

165 

1.16 

200.000 

17.5 

240 

1.20 

17.3 

235 

1.65 

250,000 

20.0 

314 

1.57 

19.8 

308 

2.15 

300,000 

22.3 

390 

1.95 

22.0 

380 

2  66 

350,000 

24.4 

467 

2.34 

24.2 

460 

3.22 

400,000 

26.4 

547 

2.73 

26.2 

539 

3.79 

450,000 

28.3 

629 

3.15 

28.0 

615 

4.30 

500,000 

30.0 

706 

3.53 

29.7 

692 

4.83 

550,000 

31.7 

789 

3.95 

31.4 

774 

5.41 

600,000 

33.3 

870 

4.35 

33.0 

855 

5.97 

650,000 

34.9 

956 

4.78 

34.6 

940 

6.59 

700,000 

36.4 

1040 

5.20 

36.1 

1023 

7.17 

750,000 

37.8 

1122 

5.61 

37.4 

1098 

7.70 

800,000 

39.1 

1200 

6.00 

38.7 

1176 

8.23 

850,000 

40.4 

1281 

6.41 

40.0 

1256 

8.75 

900,000 

41.7 

1366 

6.83 

41.3 

1339* 

9.36 

950,000 

43.0 

1452 

7.26 

42.6 

1425 

9.97 

1.000,000 

44.3 

1541 

7.70 

43.9 

1514 

10.62 

500— JP 


152 


REINFORCED    CONCRETE. 

TABLE  LIV. — HOOPED  COLUMNS;    n=12;  /c=500 


J-in.  Hooping  at  1}  ins.  centers. 


0.5%. 

0.7%. 

Safe 

Load. 

Diameter 

Area  of 

Area  of 

Diameter 

Area  of 

Area  of 

of  Hooping 

Concrete 

Steel 

of  Hooping 

Concrete 

Steel 

in  ins. 

in  sq.  ins  . 

in  sq.  ins. 

in  ins. 

in  sq.  ins. 

in  sq.  ins. 

100,000 

7.6 

45 

.226 

7.6 

45 

.32 

150,000 

10.6 

88 

.44 

10.4 

85 

.59 

200,000 

13.4 

141 

.70 

12.8 

133 

.93 

250,000 

15.4 

186 

.93 

15.2 

181 

1.27 

300,000 

17.6 

243 

1.21 

17.4 

238 

1.66 

350,000 

19.4 

296 

1.47 

19.2 

289 

2.02 

400,000 

21.4 

359 

1.79 

21.2 

353 

2.48 

450,000 

23.0 

415 

2.08 

22.8 

408 

2.86 

500,000 

24.6 

475 

2.37 

24.6 

475 

3.34 

550,000 

26.4 

547 

2.72 

26.2 

539 

3.77 

600,000 

28.0 

616 

3.08 

27.6 

598 

4.20 

650,  000 

29.4 

679 

3.40 

29.2 

670 

4.70 

700,000 

31.4 

774 

3.87 

30.6 

735 

5.15 

7510,000 

32.2 

814 

4.08 

32.0 

804 

5.65 

800,000 

33.6 

887 

4.46 

33.3 

870 

6.10 

850,000 

34.8 

951 

4.76 

34.6 

940 

6.60 

900,000 

36.2 

1029 

5.15 

35.8 

1006 

7.00 

950,  000 

37.4 

1098 

5.45 

37.2 

1086 

7.60 

1,000.000 

38.8 

1182 

5.90 

38.4 

1158 

8.10 

i-in.  Hooping  at  2  ins.  centers. 


100,000 

9.0 

64 

.32 

9. 

63 

.45 

150,000 

12.1 

115 

.57 

12. 

113 

.78 

200,000 

14.6 

167 

.84 

14.4 

163 

1.14 

250,000 

17.3 

235 

1.17 

17.0 

227 

1.58 

300,000 

19.5 

299 

1.49 

19.2 

289 

2.03 

350.000 

21.6 

366 

1.83 

21.3 

356 

2.48 

400,000 

23.4 

430 

2.15 

23.1 

419 

2.93 

450,000 

25.2 

499 

2.49 

24.9 

487 

3.40 

600.000 

27.0 

572 

2.89 

26.7 

560 

3.90 

550,000 

28.5 

638 

3.19 

28.2 

624 

4.37 

600,000 

30.1 

711 

3.55 

29.8 

697 

4.87 

650,000 

31.7 

789 

3.94 

31.4 

774 

5.40 

700,000 

33.2 

865 

4.33 

32.9 

850 

5.95 

750,000 

34.7 

946 

4.73 

34.4 

929 

6.52 

800.000 

35.9 

1012 

5.06 

35.6 

995 

6.97 

850.000 

37.2 

1086 

5.43 

36.9 

1069 

7.50 

900,000 

,   38.3 

1152 

5.76 

38.0 

1134 

7.91 

950.000 

39.6 

1231 

6.16 

39.2 

1207 

9.45 

1,000.000 

41.1 

1327 

6.63 

40.7 

1301 

10.10 

500— 


BUILDING  DESIGN  AND  CONSTRUCTION. 


153 


TABLE  LV. — HOOPED  COLUMNS;   n=15;  fe=  750. 


J-in.  Hooping  at  1}  ins.  centers. 


0.5%. 

0.7%. 

Safe 

Load. 

Diameter 

Area  of 

Area  of 

Diameter 

Area  of 

Area  of 

of  Hooping 

Concrete 

Steel 

of  Hooping 

Concrete 

Steel 

in  ins. 

in  sq.  ins. 

in  sq.  ins. 

in  ins. 

in  sq.  ins. 

in  sq.  ins. 

100,000 

10.8 

92 

.46 

10.6 

88 

.62 

150.000 

13.6 

145 

.72 

13.4 

141 

.99 

200,000 

16.0 

201 

1.00 

15.8 

196 

1.37 

250,000 

18.0 

254 

1.27 

17.8 

248 

1.74 

300,000 

20.0 

314 

1.57 

19.8 

306 

2.15 

350,000 

21.6 

366 

1.83 

21.4 

360 

2.53 

400,000 

23.2 

423 

2.11 

23.0 

415 

2.90 

450.000 

24.8 

483 

2.41 

24.6 

475 

3.32 

500,000 

26.3 

543 

2.72 

26.0 

530 

3.70 

550,000 

27.7 

603 

3.01 

27.4 

589 

4.15 

600,000 

28.9 

656 

3.28 

28.6 

642 

4.50 

650,000 

30.2 

716 

3.56 

29.8 

697 

4.95 

700,000 

31.4 

774 

3.87 

31.0 

755 

5.30 

750,000 

32.6 

835 

4.17 

32.2 

814 

5.70 

800,000 

33.6 

887 

4.43 

33.2 

866 

6.05 

850.000 

34.8 

951 

4.75 

34.4 

929 

6.50 

900.000 

35.8 

1006 

5.08 

35.4 

984 

6.90 

950,000 

36.8 

1064 

5.32 

36.4 

1040 

7.30 

1,000,000 

37.8 

1122 

5.61 

37.4 

1099 

7.70 

1-in.  Hooping  at  2  ins.  centers. 


100,000 

11.2 

99 

.50 

11.1 

97 

.69 

150,000 

14.0 

154 

.77 

13.8 

150 

1.05 

200,000 

16.3 

209 

1.05 

16.1 

204 

1.43 

250.000 

18.4 

266 

1.33 

18.2 

260 

1.62 

300,000 

20.3 

S24 

1.62 

20.1 

317 

2.21 

350.000 

22.0 

380 

1.90 

21.8 

373 

2.62 

400.000 

23.7 

441 

2.20 

23.5 

434 

3.03 

450.000 

25.2 

499 

2.50 

24.9 

487 

3.41 

500,000 

26.6 

556 

2.78 

26.5 

543 

3.80 

550,000 

28.0 

616 

3.08 

27.7 

603 

4.22 

600,000 

29.3 

674 

3.37 

29.0 

660 

4.62 

650.000 

30.6 

735 

3.68 

30.3 

721 

5.05 

700,000 

31.8 

794 

3.97 

31.4 

774 

5.42 

750.000 

33.0 

855 

4.28 

32.6 

835 

5.85 

800.000 

34.1 

913 

4.56 

33.7 

892 

6.24 

850.000 

35.2 

973 

4.86 

34.8 

951 

6.66 

900,000 

36.3 

1035 

5.17 

35.9 

1012 

7.08 

950,000 

37.3 

1093 

5.46 

36.8 

1064 

7.44 

1,000,000 

38.4 

1158 

5.79 

37.9 

1128 

7.89 

750—J' 


154 


REINFORCED    CONCRETE. 


TABLE  LVI. — HOOPED  COLUMNS;    n  =  15;   ^  =  750. 


\-\r\.   Hooping  at   1J  ins.   centers. 


0.5%. 

0.7%. 

Safe 

Load. 

Diameter 

Area  of 

Area  of 

Diameter 

Area  of 

Area  of 

of  Hooping 

Concrete 

Steel 

of  Hooping 

Concrete 

Steel 

in  ins. 

in  sq.  ins. 

in  sq.  ins. 

in  ins. 

in  sq.  ins. 

in  sq.  ins. 

100.000 

9.0 

64 

.32 

.90 

64 

.45 

150,000 

11.5 

104 

.52 

11.4 

102 

.71 

200,000 

14.0 

154 

.77 

13.8 

150 

1.05 

250,000 

15.9 

198 

.99 

15.7 

194 

1.36 

300,000 

17.8 

249 

1.24 

17.6 

243 

1.70 

350,000 

19.4 

296 

1.46 

19.3 

293 

2.05 

400.000 

21.0 

346 

1.73 

20.8 

339 

2.35 

450,000 

22.5 

398 

1.99 

22.4 

394 

2.68 

600.000 

24.0 

452 

2.26 

23.8 

445 

3.12 

550,000 

25.4 

507 

2.53 

25.1 

495 

3.46 

600,000 

26.8 

564 

2.82 

26.4 

547 

3.84 

650,000 

28.0 

616 

3.08 

27.6 

598 

4.28 

700,000 

29.2 

670 

3.35 

28.8 

651 

4.56 

750,000 

30.3 

721 

3.61 

29.9 

702 

4.90 

800,000 

31.4 

774 

3.87 

31.0 

755 

5.30 

850,000 

32.5 

830 

4.15 

32.0 

804 

5.65 

900,000 

33.6 

887 

4.43 

33.0 

855 

6.00 

950,000 

34.6 

940 

4.70 

34.0 

908 

6.35 

1,000.000 

35.6 

995 

4.95 

35.0 

962 

6.75 

|-in.  Hooping  at  2  ins.  centers. 


100,000 

9.7 

74 

.37 

9.5 

71 

.49 

150,000 

12.5 

122 

.61 

12.3 

119 

.83 

200,000 

14.8 

172 

.86 

14.6 

167 

1.17 

250,000 

17.0 

227 

1.14 

16.7 

219 

1.58 

300.000 

18.8 

278 

1.39 

18.5 

269 

1.88 

350,000 

20.4 

327 

1.64 

20.1 

317 

2.23 

400,000 

22.0 

380 

1.90 

21.7 

370 

2.58 

450,000 

23.6 

437 

2.19 

23.3 

426 

2.97 

600,000 

25.0 

491 

2.46 

24.7 

479 

3.35 

550.000 

26.3 

543 

2.72 

26.0 

531 

3.72 

600,000 

27.6 

598 

2.99 

27.3 

585 

4.10 

650.000 

28.8 

651 

3.26 

28.5 

638 

4.45 

700,000 

30.1 

712 

3.56 

29.7 

693 

4.85 

750,000 

31.2 

765 

3.83 

30.8 

745 

5.20 

800.000 

32.4 

824 

4.12 

32.0 

804 

5.63 

850.000 

33.5 

881 

4.41 

33.1 

860 

6.02 

900.000 

34.5 

935 

4.63 

34.0 

908 

6.34 

950,000 

35.6 

995 

4.97 

35.1 

968 

6.77 

1,000,000 

36.7 

105S 

5.29 

36.2 

1029 

7.20 

750— -f" 


BUILDING  DESIGN  AND  CONSTRUCTION. 


155 


TABLE  LVII. — HOOPED  COLUMNS;    n=15;  /«=7oO. 


i-in.  Hooping  at  1}  ins.  centers. 


0.5%. 

0.7%. 

Safe 

Load. 

Diameter 

Area  of 

Area  of 

Diameter 

Area  of 

Area  of 

of  Hooping 

Concrete 

Steel 

of  Hooping 

Concrete 

Steel 

in  ins. 

in  sq.  ins  . 

in  sq.  ins. 

in  ins. 

in  sq.  ins. 

in  sq.ins. 

100,000 

7.0 

38 

.19 

7.0 

38 

.26 

150,000 

9.5 

71 

.36 

9.5 

71 

.50 

200.000 

11.6 

106 

.53 

11.6 

106 

.    74 

25Q.OOO 

13.4 

141 

.71 

13.4 

145 

1.00 

300,000 

15.2 

181 

.91 

15.2 

181 

1.27 

350.000 

17.0 

-      227 

1.14 

16.9 

224 

1.55 

400.000 

18.6 

272 

1.36 

18.4 

266 

1.86 

450,000 

20.0 

314 

1.57 

19.7 

305 

2.14 

500,000 

21.4 

360 

1.80 

21.0 

346 

2.42 

550,000 

22.6 

401 

2.00 

22.3 

391 

2.74 

600,000 

23.8 

445 

2.23 

23.6 

437 

3.06 

650,000 

25.0 

491 

2.46 

24.7 

479 

3.36 

700.000 

26.4 

547 

2.74 

26.2 

539 

3.77 

750,000 

27.5 

594 

2.97 

27.2 

581 

4.06 

800,000 

28.6 

642 

3.21 

28.2 

625 

4.38 

850,000 

29.6 

688 

3.44 

29.2 

670 

4.69 

900,000 

30.6 

735 

3.68 

30.4 

726 

5.08 

950.000 

31.6 

784 

3.92 

31.4 

774 

5.40 

1,000,000 

32.6 

835 

4.17 

32.4 

824 

5.77 

i-in.  Hooping  at  2  ins.  centers. 


100,000 

8.0 

50 

.25 

8.0 

50 

.35 

150,000 

10.6 

88 

.44 

10.5 

87 

.61 

200.000 

12.8 

129 

.65 

12.7 

127 

.89 

250.000 

14.9 

174 

.87 

14.7 

170 

1.19 

300.000 

16.7 

219 

1.09 

16.5 

214 

1.50 

350,000 

18.4 

266 

1.33 

18.2 

260 

1.81 

400,000 

20.0 

314 

1.57 

19.8 

308 

2.15 

450.000 

21.5 

363 

1.82 

21.2 

353 

2.47 

500.000 

22.9 

412 

2.06 

22.6 

401 

2.79 

550,000 

24.2 

460 

2.30 

23.9 

449 

3.13 

600,000 

25.5 

511 

2.56 

25.2 

499 

3.42 

650,000 

26.7 

560 

2.80 

26.4 

547 

3.82 

700,000 

28.0 

616 

3.08 

27.7 

602 

4.20 

750.000 

29.1 

665 

3.33 

28.7 

647 

4.51 

800,000 

30.2 

716 

3.58 

29.8 

697 

4.87 

850,000 

31.3 

769 

3.85 

31.0 

754 

5.28 

900.000 

32.3 

819 

4.09 

32.0 

804 

5.63 

950.000 

33.3 

871 

4.36 

33.0 

855 

5.98 

1,000.000 

34.4 

929 

4  84 

34.0 

010 

6.37 

750— 1* 


156 


REINFORCED    CONCRETE. 


Considere's  Formula. — Considere's  empirical  formula  is 
as  follows: 

P=  1.5/c^  +  ~/s  +  2.4^f'8 (23) 

where  P=  ultimate  column  load 

fc  =  crushing  strength  of  concrete  per  unit 

x  =  percentage  of  vertical  steel  reinforcement 

y  =  percentage  of  horizontal  steel  reinforcement 

A  =  area  of  concrete  inside  the  hoops 

fs  =  elastic  limit  of  vertical  steel  reinforcement 

/'s  =  elastic  limit  of  hori7ontal  steel  reinforcement 

Table  LVIII,  based  upon  Considere's  formula,  gives  ul- 
timate loads  for  hooped  columns  as  used  in  the  American 
System  of  Reinforcing,  Chicago,  and  F.  P.  Smith  Wire  and 
Iron  Works,  Chicago,  using  high  tensile  strength  steel, 
while  the  tables  previous  to  this  one  give  safe  working 
values  and  are  based  upon  medium  steel.  The  values  in 
Table  LVIII  should  be  divided  by  four  to  give  a  working 
load.  It  may  be  added  that  this  table  is  based  upon  the 
elastic  limit  of  No.  7  wire,  which  is  90,000  Ibs.  and  with  J4- 
and  f6-in.  rods  of  40,000  Ibs.  and  /c  =  2,800  Ibs.  per  sq.  in. 

TABLE  LVII-A.— TABLE  FOR  WIRE  SPIRALS  GIVING  LENGTH  OF  WIRE  IN  FEET  PER  FOOT  OF 
HEIGHT  OF  COLUMN 


Outside 


Pitch  (taken  vertically)  from  Center  to  Center  of  Wire 


Dia.  of 
Spiral 

1* 

1H" 

IX' 

W 

1H" 

18/T 

W 

IK* 

2" 

2H" 

2M" 

1%" 

2H" 

2^" 

2^" 

2K" 

3' 

36* 

113 

101 

91 

83 

76 

70 

65 

61 

57 

54 

51 

48 

46 

43 

41 

40 

38 

34" 

107 

95 

86 

78 

72 

66 

61 

57 

54 

51 

48 

46 

43 

41 

39 

38 

36 

32' 

101 

90 

81 

73 

67 

62 

58 

54 

51 

49 

45 

43 

41 

39 

37 

35 

34 

30' 

95 

84 

76 

69 

63 

58 

54 

51 

48 

45 

42 

40 

38 

36 

35 

33 

32 

28* 

88 

78 

71 

64 

58 

55 

51 

47 

44 

42 

39 

37 

35 

34 

32 

31 

30 

26' 

82 

73 

66 

60 

55 

51 

47 

44 

41 

39 

37 

35 

33 

31 

30 

29 

28 

24.2' 

76 

67 

61 

55 

50 

47 

43 

41 

38 

36 

34 

32 

30 

29 

28 

27 

25 

22* 

70 

62 

56 

51 

46 

43 

40 

37 

35 

33 

31 

29 

28 

27 

25 

24 

23 

20' 

63 

56 

51 

46 

42 

39 

36 

34 

32 

30 

28 

27 

25 

24 

23 

22 

21 

18* 

57 

51 

46 

41 

38 

35 

33 

31 

29 

27 

25 

24 

23 

22 

21 

20 

19 

16" 

51 

45 

41 

37 

34 

31 

29 

27 

26 

24 

23 

22 

21 

20 

19 

18 

17 

14' 

44 

39 

36 

32 

30 

28 

26 

24 

22 

21 

20 

19 

18 

17 

16 

15 

14 

12* 

38 

34 

31 

28 

26 

24 

22 

20 

19 

18 

17 

16 

16 

16 

14 

14 

13 

Note. — Considere  1910:     Spiral  Columns  must  have  at  least  6  longitudinal 
rods  not  less  than  1A  of  area  of  spirals  and  at  least  0.5%  of  concrete  area. 


BUILDING  DESIGN  AND  CONSTRUCTION.         157 


TABLE  LVIII. — HOOPED  COLUMNS,  CONSIDERED  FORMULA. 
Ultimate  Loads,  High  Carbon  Steel.     For  working  loads,  divide  by  4. 


Diameter 
of 
Column 
in.  ins. 

Diameter 
of 
Spiral 
in.  ins. 

Percentage  of 
vertical 
reinforc'ment 

90,000 
No.  7  gage. 

40,000 
i-in.  round. 

40.000 
j-in.  round. 

Area=  0.023 
sq.  ins. 

Area  =0.0491 
sq.  ins. 

Area  =0.1  104 
sq.  ins. 

1  in.  pitch. 

1J  ins.  pitch. 

li  ins.  pitch. 

10 

8 

1 
2 
3 

365,000 
385,000 
405,000 

311,000 
330,000 
350,000 

407.000 
430,000 
447,500 

12 

10 

1 
2 
3 

528,000 
560,500 
590.000 

460,000 
491  ,000 
522,500 

581  ,000 
612,500 
643,000 

14 

12 

1 
2 
3 

720,500 
765,500 
810,500 

638,000 
683,500 
728,000 

784,000 
830  ,000 
875,000 

16 

14 

1 
2 
3 

941  ,500 
1  ,003  ,000 
1,064,500 

846,000 
907,000 
969,000 

1,016,000 
1,077,500 
1,139,000 

18 

16 

.1 
2 
3 

1.191,500 
1  ,272  ,000 
1,353,000 

1  ,082  ,000 
1,162,500 
1,243,000 

1,276,500 
1,367,000 
1,437,000 

20 

18 

1 
2 
3 

1,470,000 
1,572,000 
1,674,000 

1,338,000 
1,439,500 
1,541,000 

1  ,566,000 
1,668,000 
1,769,500 

22 

20 

1 
2 
3 

1,778,000 
1,903,500 
2,029,000 

1,641,500 
1,767,000 
1,893,000 

1,884,500 
2,010,000 
2,136,000 

24 

22 

1 

2 
3 

2,115,000 
2,267,000 
2,419,000 

1,964,500 
2,116,500 
2,268,500 

2,232,000 
2,384,000 
2,536,000 

26 

24 

1 
2 
3 

2,480,500 
2,661,500 
2,842,000 

2,316,500 
2,497,500 
2,678,500 

2,608,000 
2,789,000 
2,970,000 

28 

26 

1 
2 
3 

2,875,000 
3,087.000 
3,299/500 

2,697,500 
2,909,500 
3,122,000 

3,013,000 
3,225,500 
3,437,500 

30 

28 

1 
2 
3 

3,298,000 
3,544,500 
3,790,500 

3,107,000 
3,353,000 
3,599,500 

3,447,000 
3,693,500 
3.939  500 

Note. — This  table  should  be  used  only  for  those  columns  where  -7  <  18. 

a    = 


158 


REINFORCED    CONCRETE. 


TABLE  LVIII-A.— TESTS  OP  SPIRAL  REINFORCED  COLUMNS. 
All  Columns  12"  Diameter,  10  ft.  Long. 


Maximum 

Load. 

Col. 

No. 

Size  of 
Spiral 

Pitch 

Per  Cent 
of 

Concrete 
Mix. 

Age  at 
Test 

Lbs. 

Remarks. 

Wire. 

Steel. 

Days. 

Total 

perSq. 

In. 

8311 

No.  7  Wire 

Inch 

.83 

1:1:2 

60 

600.000 

5,300 

8361 

No.  7  Wire 

Inch 

.83 

1:2:4 

60 

377,000 

3,330 

8362 

No.  7  Wire 

Inch 

.83 

1:2:4 

60 

415,000 

3,680 

8371 

MWire 

Inch 

1.6 

1:2:4 

60 

603,000 

5,300 

Did  not  fail. 

8372 

MWire 

Inch 

1.6 

1:2:4 

60 

610,000 

5,400 

Did  not  fail. 

8373 

i^  Wire 

Inch 

1.6 

1:2:4 

14 

474,000 

4,200 

8382 

ysWve 

Inch 

3.6 

1:2:4 

60 

600,000 

5,300 

Not  centrally  loaded. 

8411 

No.  7  Wire 

Inch 

.83 

1:3:6 

60 

302,000 

2,660 

8412 

No.  7  Wire 

Inch 

.83 

1:3:6 

60 

(  220,000 
1  141,000 

1,950 
i,250 

Spiral. 
Stripped  off. 

8471 

MWire 

Inch 

1.6 

1:2:4 

60 

300,000 

2,650 

20  ft.  Columns. 

8472 

K  Wire 

Inch 

1.6 

1:2:4 

60 

201,000 

2,580 

20  ft.  Columns. 

8473 

^Wire 

Inch 

1.6 

1:2:4 

60 

310,000 

2,750 

20  ft.  Columns. 

Note.— Table  LVIII-A  shows  results  of  test  of  Prof.  A.  N.  Talbot  at  Urbana, 
111.,  of  Hooped  Columns  with  high  Carbon  Steel  Spirals.  Revised  to  February 
16,  1908. 


BUILDING  DESIGN  AND  CONSTRUCTION.         159 

Euler's  Formula. — Where  height  of  columns  is  over  25 
times  their  least  diameter,  Euler's  formula  may  be  used  to 
advantage: 


P-  39.48-         ,       - 

Es 

where  n  =    ~p- 

d  —  side  of  square  column 
AB  =  area  of  steel  reinforcement 

y  =  distance  of  center  of  reinforced  bars  from  the  axia» 
plane  of  column 

Instead  of  using  the  expression  j-,  Euler's  formula   uses   the 

smallest  radius  of  gyration,  which  is  a  function  of  the  moment 
of  inertia, 

Thus  for  a  square  column  we  have 

r2  __  — 
For  a  hollow  square  column 

^*4*! 

12 

For  a  round  column 

r2=  16 
For  a  hollow  round  column 

D2  4-   d* 

Euler's  formula  for  pin  ends  is 
The  breaking  load  is 


where  A  =  the  area  of  the  column  in  sq.  in. 

E  =  the  modulus  of  elasticity  in  Ibs.  per  sq.  in 
r  =  the  radius  of  gyration  in  inches 
I  =  length  of  column  in  inches 
and       P  is  expressed  in  Ibs. 


160  REINFORCED    CONCRETE. 

A  factor  of  safety  of  from  5  to  8  is  used. 
Euler's   formula  is  not  often   used   in  the   United  States, 
where  Gordon's,  Rankine's  or  Cooper's  formula  is  preferred. 

STRUCTURAL  DETAILS. 

Roofs. — Concrete  roofs  of  nearly  every  description  have 
been  built  both  abroad  and  in  America.  They  are  either 
built  the  same  as  floors  or  beams  and  girders,  for  slightly 
sloping  roofs,  or  by  means  of  floor  slabs  molded  in  situ  be- 
tween the  iron  trusses  of  the  building.  A  third  method  is 
to  place  concrete  slabs  made  at  the  factory  on  top  of  rafters 
and  then  cover  the  slabs  with  tile  or  other  protection.  For 
factories,  shops,  blast  furnaces,  mines,  steel  mills,  etc.,  where 
corrugated  iron  has  for  many  years  been  employed,  the 
latter  is  now  being  replaced  by  roofing  plates,  interlocked 
and  fastened  to  the  rafters.  This  method  was  first  patented 
by  the  author,  who  applied  it  on  roofs  of  the  Illinois  Steel 
Company's  buildings  at  Chicago,  a  cement  storage  house  at 
the  same  place,  the  large  blacksmith  shof>  of  the  C.  &  N.  W. 
railway  at  Chicago  and  to  the  company's  Pintch  gas  plant. 
The  plates  were  made  waterproof,  of  a  mixture  of  1  cement 
to  3  torpedo  sand,  2  ft.  wide,  5  ft.  long  and  only  %  in.  thick. 
They  are  self-locking  and  removable,  similar  to  corrugated 
iron  sheets.  The  reinforcement  consisted  of  a  wire  fabric, 
which  in  this  case  was  electrically  welded.  Roofs  for  saw- 
tooth factories  are  also  often  built  of  a  tile  concrete  con- 
struction laid  on  top  of  steel  rafters.  For  flat  roofs  the 
concrete  slabs  must  be  covered  by  some  composition,  while 
for  inclined  roofs,  roofing  plates  may  be  put  on  without  cov- 
ering. 

Stairs. — Reinforced  concrete  stairs  are  easily  constructed 
and  are  rapidly  coming  into  use,  even  on  existing  brick  build- 
ings where  wooden  porches  and  stairs  have  been  employed. 
There  are  five  kinds  of  stair  construction  in  reinforced  con- 
crete: 

(1)  Concrete  steps  manufactured  in  shops  and  fitted  on 
top  of  inclined  concrete  slabs. 


BUILDING  DESIGN  AND  CONSTRUCTION.         161 

(2)  Similar  steps  fitted  to  iron  stringers. 

(3)  Plain   inclined   slab   with   top   side   toothed   to  form 
risers  and  treads. 

(4)  Soffit  and  top  molded  in  connection  with  the  string- 
ers and  cast  in' one  piece.      In  this  case  the  top  is  toothed 
for   risers   and   the   soffit   may  be   either   flat   or  toothed  to 
conform  with  the  profile  of  the  top. 

(5)  Stairs    attached   to   concrete   wall    on   one   side   and 
overhanging. 

The  general  construction  of  stairs  is  based  upon  the 
same  calculations  as  have  been  presented  under  floor  beams 
and  girders  and  need  not  be  further  detailed.  A  wire  fabric 
forms  a  very  satisfactory  reinforcement  between  the  string- 
ers for  continuous  stairs,  and  one  layer  is  generally  sufficient, 
adding  to  the  cheapness  and  rapidity  of  the  construction. 

At  the  Lakeside  Hospital  in  Chicago  the  author  con- 
structed porches  along  the  rear  of  the  hospital  so  as  to  make 
verandas  on  each  floor  for  the  patients  and  have  the  con- 
struction absolutely  fireproof.  The  porches  were  10  ft.  wide 
and  40  ft.  long  and  rested  on  8x8-in.  reinforced  concrete 
columns  extending  down  to  the  foundation  in  the  basement 
of  the  building.  There  were  four  verandas  and  the  inner 
edges  rested  on  angle  irons  extending  4  ins.  into  the  brick 
building,  being  anchored  thereto.  The  stairs  were  4  ft.  wide 
and  molded  in  place,  each  with  two  stringers  supporting  a 
flat  soffit  slab  with  the  top  toothed  for  risers  and  treads. 
The  railings  were  made  of  2-in.  wrought  iron  pipe  in  the 
usual  manner,  the  posts  being  inserted  and  wedged  to 
wrought  iron  sleeves  previously  molded  into  the  concrete 
stringers  and  beams  and  the  railings  then  fastened  to  same 
and  into  the  brick  wall  of  the  building  at  both  ends  of  the 
veranda. 

Concrete  porches  and  stairs  are  rapidly  replacing  the 
common  wooden  constructions  in  the  rear  of  tenement 
houses  and  apartment  buildings  of  large  cities. 

Structural  Steel  or  Cast  Iron  Columns.— Structural  steel 
or  cast  iron  columns  are  frequently  employed  in  reinforced 


162 


REINFORCED    CONCRETE. 


concrete  structures  on  account  of  rapidity  in  erection  after 
they  have  been  delivered  on  the  premises.  If  structural 
steel  columns,  owing  to  their  smaller  floor  area,  are  em- 
ployed, Fig.  61,  gives  a  typical  view  of  the  attachment  of 
girder  and  floor  beams,  and  Fig.  62  shows  a  view  of  the 


Fig.  62.— Cast  Iron  Base 
for  Steel  Cores. 


Fig.  61.— Steel  Core  Column  Footing  and 
Bracket  for  Beam  and  Girder  Con- 
nection. 

base  for  same.  Fig.  63  indicates  the  reinforcing  of  a  heavy 
steel  floor  girder  and  a  method  of  running  the  slab  beams 
into  same.  This  construction  was  used  in  the  Eagle  Ware- 
house &  Storage  Company's  building  on  Fulton  St.,  Brook- 
lyn, N.  Y. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


163 


The  steel  columns  are  proportioned  for  working  stresses 
of  16,000  Ibs.  per  sq.  in.,  the  hollow  columns  being  filled 
with  concrete  (Fig.  64).  The  cast  iron  columns  in  this  build- 
ing are  generally  12  ins.  in  diameter  down  to  the  fourth  floor 
and  15  ins.  to  the  second  floor  with  thicknesses  varying 

"3 — -**  _«_^~^ 


Fig.    63. — Fireproofing  of  Box   Girder  and   Twin   Girder. 

from  \}/4  ins.  to  1^4  ins.  and  lengths  of  from  12  ft.  6  ins.  to 
13  ft.  They  are  of  standard  construction.  Fig.  65  shows 
flange  connections  faced  and  drilled  for  24-in.  connection 
bolts.  The  upper  ends  of  the  columns  are  special  in  that, 
above  the  beams  and  girder  seats,  they  are  made  square  out- 
side with  rectangular  openings  5  or  6  ins.  wide  and  14  ins. 
deep  in  the  face,  to  permit  the  re- 
inforcement rods  in  beams  and 
girders  to  pass  through  for  pur- 
poses of  continuity.  The  fire- 
proofing  concrete  is  extended  2 
ins.  beyond  the  flanges  and  care- 
fully finished  with  beveled  fillets. 
The  brick  walls  are  carried  at 
every  story  by  reinforced  concrete 
girders  (Fig.  66)  with  their  outer 

face  4l/2  ins.  clear  of  the  outer  face  of  the  brick  work.  The 
concrete  walls  are  12  ins.  thick  for  the  first  three  stories,  10  ins. 
for  the  next  two,  9  ins.  for  the  next  two,  and  8  ins.  for  the  upper 
story,  reinforced  with  %-in.  rods  2%  ft.  on  centers  running  hori- 
zontally and  %-in.  rods  3  ft.  on  centers  running  vertically. 


Fig.  64.— Fireproofing  and 
Filling  for  Columns. 


164 


REINFORCED    CONCRETE. 


The  author  invariably  uses  wire  fabric  for  walls,  running 
it  through  the  reinforced  concrete  columns  and  connecting 
with  floor  and  ceiling,  both  to  prevent  temperature  cracks 
and  to  guard  against  cracks  resulting  from  uneven  settling 
of  the  building  foundation. 


L 

i± 

p-.z-.v.-.-j 

j 

: 

_*.r  N* 

,  ..:, 

:ff  •• 

;  o 

^n\ 

'£% 

ii 

! 

V  » 

*T 

V—  T 

ri 

¥ 

; 

••  \ 

Fig.  65.— Special  Top  for  Cast  Iron  Column;  Column  and  Girder 
Connections. 


The  author  also  has  advocated 
a  construction  in  which  the  struc- 
tural steel,  correctly  located,  should 
be  calculated  to  assume  the  dead 
loads  of  the  building  as  well  as 
the  loads  incidental  to  the  build- 
ing erection  and  wind  pressure — 
and  afterwards  incased  in  con- 
crete in  a  manner  to  support  the 

additional  live  load.  Such  a  building  could  be  erected  with 
the  rapidity  inherent  in  the  traditional  skyscraper  and  sev- 
eral floors  put  in  simultaneously  without  waiting  for  the 
setting  of  the  column  concrete  from  floor  to  floor.  This 
construction  has  been  adopted  by  several  well  known  engi- 


Fig.    66.— Concrete   Girders 
Supporting  Brick  Walls. 


BUILDING  DESIGN  AND  CONSTRUCTION.         165 

neers.      As  an  example,  the  construction  employed  by   Mr. 
Guy  B.  Waite,  New  York  City,  is  here  illustrated. 

Fig.  67  shows  details  of  the  general  construction.  The 
original  beams  and  girders  consist  of  small  I-beams  usually 
from  4  to  5  ins.  deep,  entering  into  the  columns  and  con- 
nected to  them  by  bent  plates  and  angles.  The  column 
itself  consists  of  four  angles  latticed  together,  so  designed 
as  to  form  when  filled  with  concrete  a  reinforcement  with  a 
maximum  radius  of  gyration.  The  column  details,  of  course, 
may  be  changed.  In  such  construction  it  hardly  needs  to 


Fig.    67.— General    Structural   Details. 

be  added  that  the  support  of  molds  and  scaffolding  is  simply 
a  matter  of  hooks,  no  floor  supports  being  required. 

Bracket  Connections. — Figure  68  shows  a  typical  beam 
floor  slab  construction  with  hooped  column  supports  and 
Fig.  69  the  construction  of  the  connection.  The  brackets 
are  reinforced  by  one  or  more  corner  rods  from  f£  to  1  in. 
in  diameter  hooked  at  the  ends  to  withstand  eccentric  loads 
and  wind  pressure.  Fig.  70  shows  a  typical  footing  for  such 
a  column  on  rock.  Sometimes  the  bearing  plate  consists  of 


166 


REINFORCED    CONCRETE. 


Fig.  68. — Typical  Beam  Floor  Slab  Construction. 


BUILDING  DESIGN  AND  CONSTRUCTION.         :  V 

one  plate  the  same  as  before  quoted.      Sometimes  economy 
is  gained  by  using  short  flat  bars,  as  here  shown. 

Fig.  71  shows  a  typical  wall  beam  and  its  connection  to 
a  girder  and  bracket  to  the  column.  The  wall  beams  usually 
represent  the  entire  panel  between  the  lintel  of  one  floor 
opening  and  the  sill  of  the  opening  on  floor  above. 


Fig.  69. — Typical  Beam,  Girder 
and  Column  Connection. 


Fig-.  70. — Typical  Footing  for 
Column  on  Rock. 


EXAMPLE    OF    BUILDING   DESIGNED    ACCORDING 
TO  THE  FOREGOING  PRINCIPLES. 

In  order  to  illustrate  the  use  of  the  tables  given  under 
Building  Design,  and  to  illustrate  further  the  principles  un- 
derlying the  design  of  raft  foundations,  the  following  exam- 
ple is  given: 

Assumptions.— -It  is  required  to  design  a  warehouse,  60  by 
60  ft.  square,  6  stories  in  height,  with  basement.  (Fig.  72.)  In 
the  southeast  corner,  above  the  roof,  is  a  garner,  weighing 
with  contents  200,000  Ibs.  The  live  lond  on  floors  is  182 
Ibs.  per  sq  ft.,  and  on  the  roof  the  live  load  is  78  Ibs.  per 


168 


REINFORCED    CONCRETE. 


sq.  ft.  The  property  on  the  north  is  not  occupied,  but  must 
not  be  encroached  upon.  On  the  east  stands  a  heavy  ware- 
house without  basement,  hence  its  foundations  are  compara- 
tively shallow,  so  that  the  basement  of  the  new  building 
is  2  ft.  below  the  bottom  of  foundations  of  this  property. 

Soil  is  stratified,  sustaining  a  pres- 
sure of  5,000  Ibs.  per  sq.  ft.  Time 
prevents  the  driving  of  piling,  which 
also  would  endanger  the  adjoining 
building.  A  reinforced  concrete  mat 
and  raft  foundation  is  decided  upon. 
The  calculations,  based  upon  a  1-6 
mixture  of  Portland  cement,  sand 
and  crushed  stone  passing  a  %-in. 
ring,  are  as  follows,  for  the  first  to 
the  sixth  floors  inclusive,  assuming 
that  beams  are  spaced  7  ft.  6  ins.  on 
centers,  and  that  girders  are  spaced 
15  ft.  on  centers: 
Slabs. — Assuming  a  span  of  7  ft.  and  a  dead  load  of  64 
Ibs.  per  sq.  ft., 

182  +  64  =  246  Ibs.  per  sq.  ft. 
Referring  to  Table  L,  and  taking 

p  =  0.006  and  fc—  580,  h  =  5  ins. 
The  steel  area  per  foot  is  .288  sq.  in.,  from  same  table. 

Assuming  ^-in.   rods  as  reinforcement,  by  Table   XXXV 


Fig.  71.— Typical  Bracket 
and  Ties  at  Walls. 


The  spacing  accord- 


their  area  is  seen  to  be  0.196  sq.  ins. 
ingly  is 

0  288  *  12  =  8%  ins.  on  centers 

where  no  fabric  is  used. 

Beams.— We  approximate:  W  =  S  X  246  =  1,968  Ibs.  per 
ft.  of  beam,  including  the  weight  of  the  beam,  and  assuming 
a  beam  12  ins.  wide. 

For  1-in.  width  of  beam, 

w=  — i-  =  164  Ibs. 


BUILDING  DESIGN  AND  CONSTRUCTION.         169 


n^t^c 


Garner 

weighing 

2.00,000  Ibs. 


4-* 


---  /S'O" 

6" 


—  /S'O"  — '  -    -  —  /S'O" 


Fig.   72.— Section  Through  Building. 


170  REINFORCED    CONCRETE. 

Table  XLVI,  for  span  of  15  ft,  gives  a  depth  of  26  ins. 
for  a  load  of  174  Ibs.  For  164  Ibs.  the  depth  is'  25  ins.,  giv- 
ing a  beam  12x25  ins.,  or  12x20  ins.  below  the  slab. 

The  same  table  gives  steel  area  for  1  in.  width  between 
0.192  and  0.176;  assuming  0.190  sq.  ins., 

0.190  X  12  =  2.28  sq.  ins. 
Assuming  8  rods, 

228-^8  =  .285  sq.  ins., 
which  corresponds  to  a  diameter  of  5i  ins. 

Later  will  be  shown  that  two  extra  rods  are  laid  in  such 
beams  as  support  the  columns  on  a  cantilever.  All  rods 
are  to  be  carefully  fastened  in  a  frame  before  being  placed. 

Girders.—  1,968  X  15  =  29,520  Ibs.  concentrated  load. 

20  520  x  15 
Hence  M  =  —  :  —  |  -  X  12  =  1,328,400  in.  Ibs. 

Selecting  a  width  of  16  ins.,  the  moment  for  1  in.  width  be- 
comes 


In  Table  XLVI  we  interpolate  between  a  36-in.  depth  at 
114,694  in.  Ibs.,  and  a  30-in.  depth  at  80,125,  and  find  a  depth 
of  slightly  over  30  ins.  for  83,025  in.  Ibs.,  leaving  the  girder 
practically  16x25  ins.  below  the  slab. 

The  steel  area  for  30  ins.  depth  is  0.224  sq.  ins. 
16X0.224  =  3.584   sq.    ins. 

Assuming  8  rods,  and  consulting  Table  XXXV, 

•  'g      =  0.448  sq.  in. 

or  8  rods,  24  m-  m  diameter. 

Eight  24-in.  rods  are  accepted,  as  no  attention  has  been 
paid  to  the  fact  that  the  girder  is  continuous. 

Location  of  Stirrups.  —  The  net  span  of  the  beam  is  seen 
to  be  13  ft.  8  ins.,  the  depth  being  25  ins.  Using  Mr.  Ran- 
some's  empirical  rule  for  spacing  stirrups,  Formula  5,  Fig.  31, 


BUILDING  DESIGN  AND  CONSTRUCTION.         171 

they  would  be  located  6%  ins.,  \2l/2  ins.,  18^4  ins.,  and  25 
ins.  apart,  from  the  end  of  the  beam.  This  leaves  a  space 
of  39^  ins.  in  the  center  of  the  span,  which  is  too  great. 
To  eliminate  this,  the  spacing  adopted  is  6  ins.,  14  ins.,  20 
ins.,  and  26  ins.,  thus  making  the  central  space  32  ins.,  and 
employing  8  stirrups,  the  material  used  being  y2-\n.  square 
bars.  Stirrups  for  girders  are  calculated  and  located  in  the 
same  manner  as  for  beams. 

Wall  Girders.  —  The  load  is  one-half  the  regular  girder 
load,  or  14,760  Ibs.,  plus  the  weight  of  the  curtain  wall  be- 
tween pilasters,  which  is  13,500  Ibs. 

Formula    for    M,    with    uniform    and    concentrated    load    is 


15x12  =  967,950  in.  Ibs. 


Assuming  the  same  depth  as  for  the  other  girders,  their 
breadth  will  be 

967,950 

80,125  = 

The  steel  area  is  24  that  of  the  other  girders,  or  24  of  3.584 
sq.  ins.,  or  2.688  sq.  ins.  Choosing  six  rods,  their  diameter 
is  found  to  be  ^4  ins.  The  stirrups  and  their  spacing  are 
calculated  as  before. 

Roof  Slab. — We  will  make  the  slabs  continuous  in  both 
directions  and  omit  the  center  beams.  The  live  and  dead 
load  is 

78  +  64=142  Ibs.  per  sq.  ft. 

Since  a  more  carefully  graded  concrete  will  be  used  in  the 
roof  to  increase  its  impermeability  to  water,  the  value  for  C 
can  be  higher,  and  p  will  be  higher. 

Taking  p  =  0.008,  and  /c  =  680, 

Table  LI  gives  for  142  Ibs.  load  and  15  ft.  span,  a  depth  of 
5  ins.,  and  a  steel  area  of  0.384  sq.  in.,  or,  by  Table  XXXV, 
using  5^-in.  rods,  their  spacing  is 

0.3068 
Q  og4   X  12  =  9f  ms.  on  centers. 


172  REINFORCED    CONCRETE. 

Roof    Beams    and    Roof    Girders.  —  These    are    calculated 
alike.     Approximately 

PF  =  142  X  8.5  =  1,207   Ibs.   per  linear  foot,  including  weight 
of  beam. 

Selecting  a  width  of  10  ins., 


W---  121  Ibs. 

By  Table  XLVI,  this  corresponds  to  a  depth  of  22  ins.  The 
steel  area  is  10  X  .160  =  1.60  sq.  ins.  Assuming  6  rods,  their 
diameter  is  found,  by  Table  XXXV,  to  be  $/&  in. 

Columns.  —  We  first  make  a  column  schedule  (see  pp.  174 
and  175),  which  explains  itself.  For  tall  buildings,  it  is 
customary  to  deduct  5  per  cent  of  the  live  load  for  the  top 
floor,  10  per  cent  for  the  floor  below,  and  5  per  cent  more 
for  each  floor  except  the  first  floor,  until  50  per  cent  of  the 
live  load  has  been  deducted.  This,  however,  we  will  omit  in 
the  example,  as  it  amounts  to  very  little,  and  might  tend  to 
complicate  the  problem. 

We  will  use  a  column  with  high  carbon  wire  hooping, 
and  employ  different  percentages  of  vertical  reinforcement, 
according  to  Conside're's  formula,  and  Table  LVIII.  The 
values  in  this  table  being  ultimate,  are  divided  by  4  to  get  the 
working  stress.  The  90,000  Ibs.  for  No.  7  gage  represents 
the  elastic  limit  of  the  wire  employed.  The  other  tables  for 
column  loads  could  be  used  —  see  Table  XXVIII,  and  Tables 
LII  to  LVII. 

The  calculations  are  made,  bearing  in  mind  that  the  roof 
load  is  142  Ibs.  per  sq.  ft.,  the  floor  loads  246  Ibs.  per  sq.  ft. 
The  weight  of  the  column  is  approximate,  allowing  for  not 
having  included  brackets,  etc. 

The  spiral  in  each  case  is  2  ins.  less  in  diameter  than 
the  column  for  same,  and  all  spirals  used  are  on  1-in.  pitch, 
as  shown  in  Table  LVIII. 

Foundations.  —  From  tests,  the  bearing  power  of  the  soil 
is  found  to  be  5,000  Ibs.  per  sq.  ft.  Fig.  73  shows  the  founda- 
tion lay-out.  As  we  cannot  encroach  upon  the  adjacent 


BUILDING  DESIGN  AND  CONSTRUCTION. 


173 


property,  rafts   must  be  resorted  to  on   the  north  and   east 
sides.     Rafts  2-7,  3-8  and  15-14  are  calculated  alike. 

Raft  2-7. — The  principle  consists  in  constructing  a  base, 
the  center  of  gravity  of  which  coincides  with  the  center  of 


Fig.   73. — Foundation  Plan  Showing  Position  of  Rafts. 

gravity  of  the  two  unequal  loads.  The  calculation  becomes 
approximate  as  we  move  in  the  outside  column  1  ft.,  on 
account  of  sheet  piling,  etc.,  and  add  18  ins.  at  the  other  end 
of  the  raft  beyond  the  centers  calculated.  See  Fig.  74. 


174 


REINFORCED    CONCRETE. 


COLUMN  SCHEDULE. 


Floor. 

Loads  in  Ibs. 
per  sq.  ft. 

Columns  1,  5,  21, 
supporting  panel 
7ix7ift. 

Columr 
12,  13, 
support 
15x 

s    7,  8.  9, 
14,  17,  18, 

Columns  2,  3.  4,  10, 
6,  11,  15,  16.  22,  23, 

ing  panel 
15  ft. 

supporting  panel 
7ix  15ft. 

6th.  .  . 
5th... 
4th... 
3rd... 
2nd.. 
1:  t..  . 

Base- 
ment. 

Foun- 
da- 
tion. . 

Panel  load  .  .  . 
Column  wt..  . 

Panel  load  .  .  . 
Column  wt..  . 
Curtain  wall.. 

Panel  load  .  .  . 
Column  wt..  . 
Curtain  wall.. 

Panel  load  .  .  . 
Column  wt..  . 
Curtain  wall.. 

Panel  load..  . 
Column  wt..  . 
Curtain  wall.. 

Panel  load  .  .  . 
Column  wt..  . 
Curtain  wall.. 

Panel  load..  . 
Column  wt..  . 
Curtain  wall.  . 

At   5,000  Ibs. 
per  sq.   ft., 
or  2.5  tons. 

7,988 
1,250 

10"  sq. 
1-V  rd. 
%  "  ties 
6"  ctrs. 

4-%"rd. 
10"  sq. 

4-5£"rd. 
10*  spiral 

y^"\\l/2"  i 
1% 

4       \/A  "  rH 

31,950 
1,250 

Same  as 
col.  1, 
6th  floor. 

Same  as 
col.  1, 
3rd  floor. 

12"  spiral 
^"xlH"  P. 
1% 

A        Z/"  r(\ 

15.975 
1,250 

Same  as 
col.  1, 
6th  floor." 

Same  as 
col.  1, 
6th  floor. 

Same  as 
col.  7, 
4th  floor. 

Same  as 
col.  7. 
4th  floor. 

Same  as 
col.  1, 
basement  . 

14"  spiral 
H"*llA"  p. 
3% 
8-1^"  rd. 

16'  spiral 
K"xlH"  P. 
3% 
8    1^1$   rd 

9,238 

13,837 
1,250 
13,500 

33,200 

55,350 
3,200 

17,225 

27,675 
3,200 
13,500 

37,825 

13,837 
1,250 
13,500 

91,750 

55,350 
3,200 

59,650 

27,675 
3,200 
13,500 

66,412 

13,837 
2,450 
13,500 

150,300 

55,350 
3,200 

14*  spiral 
K"xlH"  P. 
1% 
4-5T  rd. 

16"  spiral 
M"xl>i"  p. 
1% 
4—  M'rd. 
4-y*'  rd. 

18"  spiral 
K"xlM"  P. 

1%,/» 
4—  %*rd. 

1—%"  rd. 

18"  spiral 

W-a\lA"  p. 
3% 
8—  lYs"  rd 

77.3 

sq.  ft. 

104,025 

27,675 
3.200 
13,500 

96,199 

13,837 
2,450 
13,500 

10"  spiral 
^"xl^"  P. 
2% 
4—%    rd. 

12*  spiral 
Wji\Vi"  P. 

1% 

43/ff      j 

208,850 

55,350 
3,600 

148,400 

27,675 
3,200 
13,500 

125,986 

13,837 
3,200 
15,750 

267,800 

55,350 
4,050 

192,775 

27,675 
3,600 
15,750 

158,773 

13,837 
3,600 
13,500 

14'  spiral 
#"xlH"  p. 
1% 
4-M"  rd. 

37.94 

sq.  ft. 

327,200 

55,350 
4,050 

239,800 

27,675 
3,600 
13,500 

189,710 

94.86 
tons. 

386,600 

193.3 
tons. 

284,575 

142.3 
tons. 

56.9 
sq.  ft. 

BUILDING  DESIGN  AND  CONSTRUCTION.         175 


COLUMN  SCHEDULE. — (Continued). 


Floor. 

Loads  in  Ibs. 
per  sq.  ft. 

Columns  20,  24. 
Supporting  panel 
7J  x  15  ft. 

Column  19. 
Supporting  panel 
15x15  ft. 

Column  25. 
Supporting  panel 
fj  x  7i  ft. 

6th... 
5th... 
4th.  .  . 
3rd... 
2nd.. 
1st..  . 

Base- 
ment. 

Foun- 
da- 
tion. . 

Wt.  of  garner 
Panel  load..  . 
Column  wt..  . 

Panel  load  .  .  . 
Column  wt..  . 
Curtain  wall.. 

Panel  load  .  .  . 
Column  wt..  . 
Curtain  wall.. 

Panel  load..  . 
Column  wt..  . 
Curtain  wall.. 

Panel  load  .  .  . 
Column  wt..  . 
Curtain  wall.. 

Panel  load  .  .  . 
Column  wt..  . 
Curtain  wall.. 

Panel  load... 
Column  wt..  . 
Curtain  wall.. 

At   5.000  Ibs. 
per   sq.   ft., 
or  2.5  tons. 

50,000 
15,975 
3,600 

12"  sq. 
4—  M"  rd. 

10"  spiral 
K"xlM"  p. 
1% 

A         3/"    TA 

50,000 
31,950 
3,600 

Same  as 
col.  20, 
6th  floor. 

Same  as 
col.  20, 
5th  floor. 

Same  as 
col.  20. 
3d  floor. 

Same  as 
col.  7, 
2d  floor. 

Same  as 
col.  20, 
1st  floor. 

Same  as 
col.  7, 
bast. 

20"  spiral 

£,«•* 
8—  \W  rd. 

88.2 
«q.  ft. 

50,000 
7,988 
2,450 

Same  as 
col.  1. 
6th  floor. 

Same  as 
col.  20. 
6th  floor. 

Same  as 
col.  1. 
2d  floor. 

Same  as 
col.  7. 
4th  floor. 

Same  as 
col.  20, 
3d  floor. 

Same  as 
col.  7, 
3d  floor. 

16"  spiral 
J£'xlX2"  p. 

I/O 

4    W  rd 

69,575 

27,675 
3,600 
13,500 

85,550 

55,350 
3,600 

60,438 

13,837 
2,450 
13,500 

114,350 

27,675 
3,600 
13,500 

12"  spiral 

™, 

4  —  3/"  TA 

144,500 

55,350 
3,600 

90,225 

13,837 
3,200 
13,500 

159.125 

27,675 
3,600 
13.500 

14"  spiral 
M"xlX2"  p 
1%, 
4—  W  rd. 

16"  spiral 
W*\W  P 
1% 
4—  %,    rd. 
4—%"  rd. 

16"  spiral 
M"xlM"  P. 
3% 
8—1"  rd. 

18"  spiral 
M"xlM"  P. 

2% 

203,450 

55,350 
3,600 

120,762 

13,837 
3,200 
13,500 

203,900 

27,675 
3,600 
13,500 

262,400 

55,350 
4,000 

151,299 

13,837 
3,600 
13,500 

248,675 

27,675 
4,000 
15,750 

321,750 

55,350 
4,800 

182,236 

13,837 
4.000 
15,750 

296,100 

27,675 
4,000 
13,500 

381,900 

55,350 
4,000 

215,823 

13,837 
3,600 
13,500 

341,275 

170.6 

tons. 

68.25 
sq.  ft. 

441,250 

220.6 
tons. 

246,760 

123.4 
tons. 

49.4 
sq.  ft. 

17,6 


REINFORCED    CONCRETE. 


Fig.  74.— Diagram  for  Raft  2-7. 

Load  column  2  =  284,575  Ibs. 
Load  column  7  =  386,600  Ibs. 

Sum =671,175  Ibs. 

Dividing  by  5,000  =  134.23  sq.  ft. 


Area  of  raft 


X  14  =  134.23. 


19.18. 


ll~ 


284575 
671175 


X  14 


5.94. 
262 


—     o      A     i   J-.       —     o       -into     —  O."4. 


3    bt  +  ba  —  3     19.18 
Solving,  b2  =  5.22,  and  bi  =  13.95. 

To  find  the  cross-section  of  raft,  we  must  find  the  center 
of  gravity  of  one-half  the  trapezoid,  which  gives  the  leverage 
for  the  bending  moment,  as  follows: 

b1  —  b,  =  13.95  -  5.22  =  8.73. 
63  —  b2  _  l^  _  8.06 
~1T7T  ==  14  =  T4  ' 
63  _  &2  =  5.03. 
5.03  +  5.22  =  10.25. 


10.25  +  2x5.22 


10.25  +  5.22 


=  3.59. 


BUILDING  DESIGN  AND  CONSTRUCTION.        177 

In  like  manner,  solving  for  15 

Z5  =  3.12. 

Let  A  =  area  of  entire  trapezoid,  and  a  =  the  area  of  that 
part  to  the  left  of  the  center  of  gravity,  CG,  then 

M  =Wk-(W  +  Wl)k=  Wl  h  -  —        (W  +  Wl)  k  - 


2,294,800  —  1,120,750  =  1,174,050  ft.  Ibs.* 

This  is  1,174,050  x  12  =  14,088,600  in.  Ibs.  Per  inch  of 
width  this  is 

14088600 
1025  1<12  =  114>540in.lbs. 

We  will  choose  n  =  15,  as  E0  for  concrete  in  a  comparatively 
large  mass  is  nearer  2,000,000. 

Choosing  p  =  0.01,  we  find,  from  Table  XXXIX, 

1  —  j  =0.861. 
Substituting  in  Formula  (11), 

M,=  /;<!—  f  )W« 

Mfl  =  0.01  X  16,000  X  0.861  X  1  X  d*. 

Whence  d  =  29  ins. 

Adding  2  ins.,  we  get  &  =  31  ins.,  for  the  slab,  and  the 
steel  area  is  0.01  X  29  =  0.29  sq.  ins.  per  in.  and  0.29  X  12  =  3.48 
sq.  ins.  per  ft,  or,  according  to  Table  XXXV,  l^-m.  rods. 
4^  ins.  on  centers. 

For  compression,  by  combining  Formulas  (10)  and  (11), 

pf.      0.01   x   16000 
i/c*  =  #,or/0=p=       ^  x  Q  41? 

fc  =767  Ibs.  per  sq.  in.,  which  is  safe. 

If,  however,  we  specify  a  maximum  safe  load  in  compres- 
sion of  500  Ibs.,  we  find  the  reinforcement  as  follows: 

*  These  figures  are  obtained  by  using  greater  accuracy  in  the  measure- 
ments,  than  the  2  places  of  decimals  here  given. 


178  REINFORCED    CONCRETE. 

767  —  500  =  267  Ibs.  excess. 

267  x  w  _  267  x  SiiZJLl9  =  1617  ,bs. 

1  A 1  7 

1  fiOOO  =  ^  scl'  *ns'  remf°rcernent  required  for  each  one-inch 
in  width,  or  approximately  1-in.  rods  every  8  inches. 

The  distributing  rods  under  column  7  are  approximated  as 
follows.*  see  Fig.  75 : 


r 

u  r 
*  ^ 

a 


/4* 


Fig.   75. — Diagrams  for  Foot  of  Columns  7  and  2. 

386600        6 
M  = g X  77  X  12  =  7,000,000  in.  1H 

Assuming  a  width  of  36  ins.,  each  inch  would  have  a  moment  of 

7000000 
M  = ^6 =  194,000  inch  Ibs. 

By  Table  XLVI,  this  gives  a  depth  of  46  ins.,  with  a  steel  area 
of  0.34  sq.  ins.  for  each  inch  width. 

36  X  0.34  =  12.24  sq.  in.,  which  by  Table  XXXV  gives  12 
rods,  Ir3g  ins.  in  diameter  (laid  in  two  courses). 

Similarly,  for  column  2, 

M^  ^j^~  x  ~  x  12  -  1,370,000  in.  Ibs. 
For  a  width  of  24  ins.,  this  gives  per  inch, 

57,000  in.  Ibs. 

*  To  gain  practice  m  using  tables,  we  here  use  Table  XLVI.  where  «  »  IU 
and  p  =  0.008,  instead  of  15  and  0.01  respectively. 


BUILDING  DESIGN  AND  CONSTRUCTION.         179 

This  corresponds  to  a  depth  of  26  ins.  and  a  steel  area  of 
0.192  s<j.  ins.,  or  1^-in.  rods  6  ins.  on  centers.  However,  this 
depth  will  be  taken  at  31  ins.,  the  same  as  the  slab. 


r 


14' O" 


—  /6'  6*     — 

Fig.    76.— Plan  and   Section  of  Raft  2-7. 

The  raft  2-7  will  therefore  be  shown  as  in  Fig.  76,  the 
decimals  being  replaced  by  feet  and  inches. 

Rafts  3-8  and  15-14  are  like  raft  2-7,  and  raft  1-6  is  calcu- 
lated in  a  similar  manner. 


180 


REINFORCED   CONCRETE. 


Quadrilateral   Raft   4-5-9-10.— See   Fig.    77.     The   outside 
columns  are  each  moved  in  1  ft. 


Fig.  77.— Diagram  for  Raft  4-5-9-10. 

4  =  284,575  Ibs. 

5  =  189,710  Ibs. 
9  =  386,600  Ibs. 

10  =  284,575  Ibs. 

1,145,460  Ibs. 
1,145,460  -r-  5,000  =  229.1  sq.  ft. 

The  center  of  gravity  between  4  and  10  is  at  the  center  of  a 
line  connecting  them,  at  point  A,  which  represents 
2X284,575  =  569,150  Ibs. 

5  =  189,710 

9  =  386,600 


189710 
ll  ~  ,576310 


x  14  x 


£  =  576,310 

=  6.52,  which  makes  the  distance 


between  A  and  B,  3.38  ft. 

5691  50 
From  B  to  C  =    i14546Q    X  3.38  =  1.68  ft. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


181 


3.38 — 1.68=1.7,  which  locates  the  center  of  gravity,  C, 
of  the  entire  raft. 

Enough  area  is  added  along  AD  so  that  the  center  of 
gravity  of  the  quadrilateral  may  be  at  C.  This  additional 
distance  DE  is  3  X  1.7  =  5.1  ft. 

The  added  area  is  5.1  X   y  x  1.414  =  50  sq.  ft. 

Area  square  4-5-9-10  is  14  X  14=196  sq.  ft.  196  +  50  =  246 
sq.  ft,  which  is  over  229  sq.  ft.  and  therefore  safe. 

The  same  method  as  was  employed  for  raft  2-7  will  give 
the  section  and  reinforcement  for  raft  4-5-9-10.  The  raft,  as 
constructed,  will  measure  15  ft.  6  ins.  on  the  north  and  east 
sides,  as  shown  in  Fig.  77. 

Square  Footings,  12,  13,  17  and  18.— See  Fig.  78.  Since 
the  area  required  is  77.3  sq.  ft.,  the  side  is 


Rods  l"cc &"o.c. 
•  in  4-  directions 


^77.3  =  8  ft.  9  in.  X8  ft.  9  in. 

With  a  column  20  ins.  in  diameter,  its  area 
is  2.17  sq.  ft.    The  load  is  386,600  Ibs. 

2.17  X  5,000  =  10,850  Ibs. 
386,600  —  10,850  =  375,750  Ibs. 
375750  . ,  81 
4 

The  width  of  the  imaginary  beam  being 


Fig. 

Footings  12,  13, 


78. —  Plan    of 
tings  12,  1 
17  and  18. 


8.75  X  12 
3 


35, 


we  have  the  moment  per  inch  width 


1,232,930 
35 


=  35,227  in.  Ibs. 


which,  according  to  Table  XLVI,  by  interpolation  between 

33,113,/i=20" 
and  40,880,  h=22" 


182  REINFORCED    CONCRETE. 

gives  us  h  =  21"  as  thickness  of  slab,  and  0.157  sq.  ins.  rein- 
forcement per  inch  width,  or 

1"  c.  c.  rods  5"  on  centers  in  4  directions. 

Similar  calculations  will  give  figures  for  the  other  square 
footings. 

The  above  calculations  are,  of  course,  approximate,  but 
they  are  safe,  and  are  as  simple  as  any  calculations  the 
author  has  seen. 

Conclusion. — The  mat  reinforcement  consists  of  a  6x6-in. 
mesh  high  carbon  steel  fabric  of  No.  7  and  No.  11  gage  wire, 
laid  within  2  ins.  of  the  top  of  the  6-in.  floor,  depressed  under 
the  columns  to  about  5  ins.  below  the  floor. 

Before  excavation,  sheet  piling  should  be  carefully  driven 
along  the  north  and  east  building  lines,  the  basement  col- 
umns being  here  moved  in  12  ins.  The  retaining  walls  run 
from  column  to  column,  and  above  the  sheet  piling  are  built 
out  to  the  building  line.  The  fabric  continues  from  the  mat 
up  within  2  ins.  of  the  inside  of  the  retaining  wall,  and  to  it 
is  wired  such  reinforcing  rods  as  are  required  to  withstand 
the  earth  pressure  from  the  adjacent  property. 

The  first  story  columns  are  placed  on  the  building  line, 
by  cantilevering  the  girders  12  ins.  It  will  be  found  that  the 
steel  above  calculated  will  take  care  of  this  cantilever  action, 
but  the  author  always  adds  two  more  rods  at  the  bottom  of 
the  girders,  bent  at  1/3  the  span  and  reaching  the  top  at  each 
end. 

The  curtain  walls  are  reinforced  with  fabric  only  and  are 
6  ins.  thick. 

Where  the  building  ordinances  permit  it,  the  author  uses 
a  high  carbon  wire  fabric,  deducting  the  strength  of  same 
from  the  required  steel  area;  for  instance,  in  calculating  1st 
to  6th  floors,  we  had,  steel  area  =  0.288  sq.  ins.  per  foot.  For 
4x6-in.  No.  7  gage  we  have 

3X0.0254  =  0.0762. 


BUILDING  DESIGN  AND  CONSTRUCTION.         183 

Safe  strength,  28,000  Ibs.  makes  it  equal  to  twice  the  area 
at  14,000  Ibs.,  or  0.1524  sq.  in.  Hence  the  steel  area  required  is 

0.2880  —  0.1524  =  0.1356 
Using  r/2-in.  rods  as  before, 

0.196 

X  12  =  l?i  ins.  on  centers, 


instead  of  8^  ins.,  and  if,  owing  to  the  increased  lateral  con- 
tinuity, we  use 

wP       wP 
M  =  14  or  16  ' 

still  lighter  steel  areas  will  be  found,  and  have  been  success- 
fully used  in  carefully  executed  work.     See  Table  XLV. 

SEQUENCE  OF   OPERATIONS   IN   CONSTRUCTION. 

While  in  brick,  masonry  or  structural  steel  construction 
the  engineer  has  to  do  with  first-class  mechanics  skilled  in 
their  work,  in  reinforced  concrete  construction  most  of  the 
actual  placing  of  the  work  is  left  to  laborers  who  are  often 
unskilled  foreigners  hardly  able  to  understand  the  English 
language.  The  foremen,  while  probably  good  mechanics, 
may  have  no  experience  in  this  particular  branch.  The  engi- 
neer must  therefore  fortify  the  contractor  by  a  very  rigid  and 
exacting  specification,  which  is  to  be  literally  followed  in 
every  minute  detail.  The  contractor  in  turn  must  impress 
the  importance  of  the  specification  and  the  detail  plans  on 
his  superintendent  and  foremen,  and  these  in  turn  must  ex- 
plain and  show  the  mechanics  exactly  what  is  wanted,  and 
so  organize  their  work  that  the  same  men  can  do  the  same 
work  over  and  over  again,  until  they  learn  it.  No  method 
of  construction  needs  more  careful  organization  of  the  work 
at  the  building  site  than  reinforced  concrete. 

Clearing  the  Site.  —  The  first  work  in  any  construction  is 
generally  excavation.  The  author  has  found  the  following 
a  valuable  rule  where  excavation  is  necessary.  The  site 
should  be  kept  as  clear  of  machinery  as  possible;  boilers, 
engines,  mixers,  and  even  crushers,  should,  if  practicable,  be 
placed  at  the  side  of  the  building  or  on  a  suitably  constructed 


184  REINFORCED    CONCRETE. 

bridge  floor  or  preferably  in  an  adjacent  lot  leased  for  the 
purpose.  This  keeps  the  excavated  premises  clear  of  incum- 
brances,  except  large  derricks  arranged  to  reach  every  corner 
of  the  site,  thus  saving  the  moving  of  the  contractor's  plant. 
The  selection  of  such  plant  depends,  of  course,  upon  the 
contractor's  method  of  construction. 

Lumber  and  Reinforcing  Materials. — The  contractor  must 
plan  for  the  delivery  of  materials  on  the  premises  sufficiently 
ahead  of  time  to  prevent  any  stoppage  of  the  work.  The 
first  material  needed  on  the  premises  is  lumber  for  the  forms. 
For  a  large  sized  job  it  is  well  to  have  a  band  saw,  cross-cut 
saw,  and  a  boring  machine  driven  by  a  small  motor  for  the 
manufacture  of  parts  of  the  different  forms,  which  may  then 
be  numbered  and  piled  for  future  use  in  places  readily  ac- 
cessible at  that  time.  The  reinforcing  material  should  com- 
mence to  arrive  simultaneously  with  the  lumber  and  be  deliv- 
ered in  the  order  in  which  it  is  to  be  used,  and  numbered 
and  placed  in  racks  easily  accessible.  As  soon  as  the  exca- 
vation is  ready  the  first  forms  are  assembled  and  erected, 
and  the  reinforcement  carefully  placed  and  fastened  in  posi- 
tion. 

Placing  the  Reinforcement. — Before  depositing  the  con- 
crete, the  forms  are  swept  clean  and  sprinkled,  and  a  man 
appointed  by  the  foreman  for  the  purpose  gives  all  his  time 
to  the  inspection  of  the  proper  location  of  all  reinforcement. 
In  the  placing  of  reinforcing  material,  Hennebique  gen- 
erally proceeds  as  follows:  A  bed  of  concrete  is  first  placed 
in  the  bottoms  of  the  beam  and  girder  molds,  upon  which  is 
laid  the  tension  bars  with  the  stirrups  slipped  under  them 
and  held  in  upright  position  by  small  mounds  of  concrete 
packed  around  their  bottoms.  The  remaining  concrete  is 
then  placed  and  rammed  in  3-in.  layers  until  the  level  of  the 
floor  slab  is  reached.  The  reinforcing  rods  and  stirrups  of 
the  slab  are  then  blocked  up  on  a  bed  of  concrete  exactly  as 
in  constructing  the  girders.  Care  is  taken  that  the  stirrups 
are  kept  in  contact  with  the  tension  bars  and  that  neither  is 
disturbed  or  shifted  by  the  process  of  ramming. 


BUILDING  DESIGN  AND  CONSTRUCTION.         185 

Instead  of  placing  the  reinforcement  piece  by  piece  as 
herein  described,  the  author  prefers  and  recommends  the 
practice  of  erecting  the  skeleton  complete  before  any  con- 
crete is  placed,  as  indicated  in  Fig.  79,  which  shows  work  at 
the  Winton  Garage,  Chicago.  The  cut  shows  the  built-up 
reinforcement  of  the  girders  in  position,  and  the  hooked 
rods  laid  into  the  end  wall  ready  for  concreting. 


Fig.  79.— Reinforcement  of  Girders  in  Winton  Garage,  Chicago. 

Making  Concrete. — The  sand,  stone  and  cement  must  be 
located  where  they  can  be  dumped  from  wagons,  and  with 
one  handling  delivered  to  the  mixer.  The  distribution  of  the 
materials  to  the  mixer  must  be  carefully  watched,  as  it  must 
always  be  kept  in  mind  that  a  building  is  only  as  strong  as 
its  weakest  part  and  the  omission  of  a  few  bags  of  cement 
in  the  batch  would  be  a  matter  of  the  greatest  consequence. 


186  REINFORCED    CONCRETE. 

Delivering  Concrete. — From  the  mixer  the  concrete  should 
be  delivered  to  the  wheelbarrows,  buckets,  or  conveyors  as 
fast  as  made,  and  at  the  same  time  as  fast  as  required.  As 
the  mixer  is  generally  located  stationary  at  one  level,  the 
delivery  from  the  mixer  to  the  different  floors  means  the 
introduction  of  a  vertical  lift  or  elevator  and  here  the  con- 
crete is  either  transported  in  barrows  or  buckets,  which  are 
hoisted  on  an  elevator  platform  or  in  bulk  by  means  of  ele- 
vator buckets  on  an  endless  chain.  When  the  concrete  has 
arrived  at  its  proper  level,  it  is  either  wheeled  by  hand  to 
the  forms,  or  the  buckets  are  moved  by  derricks,  cableways 
or  otherwise,  but  the  work  should  be  so  arranged  that  there 
is  no  stop  or  waiting.  Some  process  must  be  going  on  con- 
tinually. 

Depositing  Concrete. — The  different  types  of  construction 
require  different  consistencies  of  concrete  and  the  method  of 
depositing  varies  accordingly.  In  cold  weather  a  rather  dry 
mixture  should  be  employed  and  should  be  poked  well  around 
the  reinforcement  and  carefully  tamped  with  heavy  iron 
tampers.  In  hot  weather  a  more  wet  consistency  can  and 
should  be  used,  in  which  case  the  concrete  is  stirred  or 
spaded  around  the  reinforcement  and  adjacent  to  the  forms. 
The  compacting  of  floor  slabs  is  sometimes  done  by  rolling, 
first  by  using  a  3x3-ft.,  350-lb.  wooden  roller,  then  a  2^x2^- 
ft,  500-lb.  iron  roller  and  finally  a  2^x2^-ft,  700-lb.  iron 
roller.  It  must  always  be  remembered  that  the  hardening 
of  concrete  is  not  a  "drying-out  process,"  as  some  are  apt  to 
suppose,  but  is  a  chemical  action  caused  by  the  addition  of 
water  to  the  cement.  The  concrete  takes  its  "initial  set"  in 
a  short  time  and  therefore  should  be  deposited  in  place  as 
quickly  after  mixing  as  possible. 

Concreting  Columns. — Column  molds  are  often  built  up- 
wards while  the  concreting  progresses;  usually,  However,  the 
form  is  erected  complete  the  full  height,  and  the  concrete 
filled  in  from  the  top.  In  this  case  one  side  of  the  mold  is 
left  loose  at  the  bottom  so  the  form  may  be  carefully  in- 
spected as  to  location  of  reinforcement  and  all  shavings,  etc., 


BUILDING  DESIGN  AND  CONSTRUCTION 


187 


removed  from  the  bottom  before  the  concrete  is  poured  in. 
Long-handled  rammers  or  spading  tools  are  run  up  and  down 
the  side  of  the  form  during  the  concreting  to  prevent  air 
voids  or  exposure  of  aggregates. 

Concreting  Walls.— In  Fig.  80  is  shown  the  wall- 
form  employed  in  constructing  the  wall  of  the  Central  Felt 
&  Paper  Co.'s  factory,  Long  Island  City,  N.  Y.  The  walls 
are  6  ins.  thick  between  wall  columns  and  carry  no  weight 
except  their  own,  and  the  adjacent  edges  of  the  floor  and  roof 
slabs.  At  the  floor  and  roof  lev- 
els and  also  at  the  bottom,  each 
wall  bay  is  reinforced  as  a  girder. 
The  reinforcement  of  the  wall 
consists  of  vertical  sheets  of  wire 
fabric  placed  near  the  inner  sur- 
face. At  window  or  door  open- 
ings this  fabric  is  folded  back  so 
as  to  form  a  U-shaped  net  at  the 
side  of  each  opening.  Sheets  of 
the  same  material  bent  to  U- 
shape  are  also  embedded  in  the 
wall  concrete  under  the  window 
sill.  Each  panel  of  the  form  con- 
sists of  two  vertical  pieces  3  ft. 
high  and  16  ft.  long.  For  the 
first  course  they  were  seated  at 
the  floor  level  and  braced  by  props 
on  both  sides.  After  the  concrete 
had  stood  for  three  days  the  panels 
were  loosened  and  raised  until  the  lower  edges  were  2  ins. 
below  the  top  of  the  concrete.  In  this  position  they  were 
supported  by  bolts  running  through  sleeves  resting  on  the 
top  of  the  concrete  and  the  upper  edges  were  held  by  trans- 
verse boards  nailed  4  ft.  apart.  The  sleeves  used  consisted 
of  pasteboard  tubes,  it  being  found  that  these  were  just  as 
efficient  and  much  easier  to  place  and  trim  than  wrought-iron 
pipe. 


Fig.  80.— Wall  Mold,  Central 
Felt  &  Paper  Co.  Factory. 


188  REINFORCED    CONCRETE. 

Several  designs  for  detachable  wall  form  ties  have  been 
devised,  and  used  with  more  or  less  success.  The  simplest 
method  seems  to  be  either  the  one  used  at  the  Central  Felt 
&  Paper  Co.'s  factory,  or  simply  to  employ  soft  iron  tie  wire 
holding  the  outside  studs  together,  leaving  the  tie  wires  in 
the  concrete  by  clipping  off  the  wire  in  taking  off  the  forms. 
For  walls  the  concrete  is  generally  run  in  fairly  wet  and  in 
place  of  tamping  is  usually  stirred  with  rods,  and  the  rein- 
forcing fabric  shaken  or  lightly  tapped. 

Joining  Successive  Days'  Work. — When  the  concreting  of 
a  structure  cannot  be  made  a  continuous  process  from  start 
to  finish,  as  is  often  the  case,  care  must  be  exercised  in  stop- 
ping off  one  day's  work  and  in  joining  the  next  day's  work 
to  the  break.  In  no  case  must  the  concrete  be  stopped  before 
the  full  depth  of  the  floor  has  been  completed  over  the  area 
of  section  for  one  day's  work.  The  joint  should  take  place 
along  the  center  line  of  the  span  for  a  slab  or  in  the  center 
of  span  of  a  girder  and  the  joint  be  made  fairly  square  but 
as  rough  as  possible.  Fig.  81  shows  in  the  foreground  a  piece 
of  a  2x4-in.  scantling  braced  up  for  a  joint  in  the  slab  work. 
The  next  day  this  joint  is  cleaned  by  hose  and  sprinkled  with 
neat  cement  before  depositing  the  concrete.  Some  contract- 
ors prefer  the  joint  to  be  made  at  supports,  but  the  author 
has  avoided  cracks  by  making  joints  where  concrete  on  top  is 
in  compression.  If  the  joint  is  made  at  the  support,  it  should 
be  made  along  the  longitudinal  center  line  of  the  girder  or 
beam. 

Protection  of  Concrete  in  Setting. — Now  comes  a  very 
important  point.  To  enable  the  concrete  to  set  properly  it 
must  be  kept  moist.  This  is  an  item  which  too  often  is 
neglected  and  which  prevents  many  otherwise  well-designed 
reinforced  concrete  constructions  from  attaining  the  strength 
intended.  A  layer  of  moist  sand  or  preferably  sawdust  should 
be  spread  over  all  horizontal  surfaces  and  kept  moist  for  a 
week  or  ten  days,  and  all  vertical  surfaces  should,  after  re- 
moval of  forms,  be  kept  wet  by  sprinkling  or,  if  the  surfaces 
are  exposed  to  the  sun,  should  be  covered  with  canvas  which 


BUILDING  DESIGN  AND,  CONSTRUCTION.         189 

is  kept  wetted  down  by  means  of  a  hose.  Such  a  method  is 
illustrated  by  Fig.  154,  under  Tanks. 

Protection  Against  Freezing. — Concrete  work  is  often  car- 
ried on  ia  winter  months  and  will  freeze  if  precautions  are 
not  taken.  The  freezing  retards  the  setting  of  the  concrete 
and  often  completely  ruins  it.  It  is  usually  best  to  remove 
any  concrete  known  to  have  been  frozen.  Simple  precautions 
can  be  taken  to  prevent  freezing,  such  as  heating  the  mate- 
rials, adding  less  than  10  per  cent  of  salt  to  the  water,  keep- 
ing the  building  heated  by  means  of  salamanders,  and  cover- 
ing the  concrete  after  being  laid  with  some  good  insulating 
material,  such  as  cement  bags,  straw,  manure,  etc. 

If  work  must  be  done  in  cold  weather  the  only  proper 
method  is  to  inclose  the  building  in  temporary  walls  of  can- 
vas or  boards  and  roof  it  over;  if  necessary,  cover  all  open- 
ings with  light  duck,  and  all  floors  as  soon  as  laid,  with  plank 
panels  raised  some  6  ins.  above  the  floor  surface.  Steam  pipes 
can  then  be  run  into  each  floor  from  a  boiler  employed  for 
the  purpose.  The  same  boiler  may  be  used  to  heat  the  sand, 
stone  and  water  and  the  exhaust  steam  may  be  discharged 
into  the  rooms  and  under  the  floor  covering  to  heat  them 
and  keep  the  air  moist.  This  will  assist  in  quickly  hardening 
the  concrete  during  cold  weather. 

It  is  under  all  circumstances  preferable  not  to  continue 
concrete  work  in  cold  weather,  as  it  prevents  the  proper 
wetting  of  the  concrete  while  setting. 

FORMS,    MOLDS,    CENTERING,    AND    FALSEWORK. 

Forms,  molds,  and  centering  designate  the  temporary  con- 
struction required  to  give  to  the  concrete  its  shape.  False- 
work is  generally  used  to  designate  the  supports  of  forms, 
molds,  and  centering.  In  considering  this  subject  we  will  use 
the  expression  "forms"  to  include  all  the  items  here  men- 
tioned. 

Inasmuch  as  forms  represent  most  of  the  labor  entering 
into  the  cost  of  reinforced  concrete,  they  should  be  carefully 
designed  in  the  drafting  room  and  not  by  rule  of  thumb. 


190 


REINFORCED    CONCRETE. 


The  best  contractors  carefully  design  the  forms  with  a  view 
of  obtaining  maximum  safety  and  economy. 

Kind  of  Lumber. — White  pine  should  be  first  choice; 
next  come  spruce,  fir,  Norway  pine  or  southern  pine. 
The  lumber  should  not  be  kiln-dried,  but  should  be 
dried  stuff.  Painting  forms  with  pararfine  oil  will 
prevent  swelling.  Beveled  edges  or  tongue  and  groove 
TABLE  LVIII-B.— SAFE  LOADS,  UNIFORMLY  DISTRIBUTED  FOR  RECTANGULAR  SPRUCE  OR 
WHITE  PINE  BEAMS  ONE  INCH  THICK.  FROM  "CARNEGIE." 


Span 
in 
Feet. 

Depth  of  Beam. 

6" 

7* 

8" 

9" 

10" 

11" 

12" 

13* 

14" 

15" 

16' 

5 

600 

820 

1070 

1350 

1670 

2020 

2400 

2820 

3270 

3750 

4270 

6 

500 

680 

890 

1120 

1390 

1680 

2000 

2350 

2730 

3120 

3560 

7 

430 

580 

760 

960 

1190 

1440 

1710 

2010 

2330 

2680 

3050 

8 

380 

510 

670 

840 

1040 

1260 

1500 

1760 

2040 

2340 

2670 

9 

330 

460 

590 

750 

930 

1120 

1330 

1560 

1810 

2080 

2370 

10 

300 

410 

530 

670 

830 

1010 

1200 

1410 

1630 

1880 

2130 

11 

270 

370 

490 

610 

760 

920 

1090 

1280 

1490 

1710 

1940 

12 

250 

340 

440 

560 

690 

840 

1000 

1180 

1360 

1560 

1780 

13 

230 

310 

410 

520 

640 

780 

930 

1080 

1260 

1440 

1640 

14 

210 

290 

380 

480 

590 

720 

860 

1010 

1170 

1340 

1530 

15 

200 

270 

360 

450 

560 

670 

800 

940 

1090 

1250 

1420 

16 

190 

260 

330 

420 

520 

630 

750 

880 

1020 

1180 

1330 

17 

180 

240 

310 

400 

490 

590 

710 

830 

960 

1100 

1260 

18 

170 

230 

290 

370 

460 

560 

670 

780 

910 

1040 

1190 

19 

160 

210 

280 

360 

440 

530 

630 

740 

860 

990 

1130 

20 

150 

200 

270 

340 

420 

510 

600 

710 

820 

940 

1070 

21 

140 

190 

260 

320 

390 

480 

570 

670 

780 

890 

1020 

22 

140 

190 

240 

310 

380 

460 

540 

640 

740 

850 

970 

23 

130 

180 

230 

290 

360 

440 

520 

610 

710 

810 

920 

24 

130 

170 

220 

280 

350 

420 

500 

590 

680 

780 

890 

25 

120 

160 

210 

270 

330 

410 

480 

560 

660 

750 

860 

26 

110 

160 

210 

260 

320 

390 

460 

540 

630 

720 

820 

27 

110 

150 

200 

250 

310 

370 

440 

520 

610 

690 

790 

28 

110 

140 

190 

240 

300 

360 

430 

500 

580 

670 

760 

29 

110 

140 

180 

230 

290 

350 

410 

490 

560 

640 

740 

For  oak  increase  values  in  table  by  l/^. 

For  yellow  pine  increase  values  in  table  by  2/$. 

To  obtain  safe  load  for  any  thickness:  Multiply  values  for 
1  inch  by  thickness  of  beam. 

To  obtain  the  required  thickness  for  any  load:  Divide 
by  safe  load  for  1  inch. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


TABLE  LVIII-C.— SAFE  LOADS  FOR  RECTANGULAR  WOODEN  PILLARS  (SEASONED). 
FROM  "CARNEGIE." 

/  =  length  of  pillar  in  inches. 
d  =  width  of  smallest  side  in  inches. 


Ratio  of  Length 

Safe  Loads  in  Pounds  per  Square  Inch  of  Section. 

to  Least  Side 

/ 
d 

Yellow  Pine 
(Southern). 

White  Oak. 

White  Pine  and 
Spruce. 

12 

995 

818 

707 

14 

955 

785 

679 

16 

913 

750 

649 

18 

869 

715 

618 

20 

825 

678 

587 

22 

781 

642 

556 

24 

738 

607 

525 

26 

697 

575 

495 

28 

657 

541 

467 

30 

619 

509 

440 

32 

583 

479 

414 

34 

549 

451 

390 

36 

516 

425 

367 

38 

487 

400 

346 

40 

458 

377 

326 

192 


REINFORCED    CONCRETE. 


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BUILDING  DESIGN  AND  CONSTRUCTION.         193 

stuff  gives  the  best  results  for  floor  and  wall  forms.  Table 
LIX  gives  safe  working  stresses  for  various  kinds  of  timber. 
It  should  be  borne  in  mind  that  this  table  is  arranged  for 
use  in  designing  trestles,  which  are  permanent  structures, 
having  to  sustain  weight  not  only  temporarily,  as  in  concrete 
falsework,  but  allowance  is  also  made  for  the  possible  de- 
terioration of  the  timber.  In  concrete  molds,  however,  much 
higher  values  can  be  assumed  for  the  stress  in  the  lumber, 
since  the  time  the  timber  is  in  place  is  a  comparatively  short 
time,  and  another  fact  which  lessens  the  stresses  is  that  con- 
crete begins  to  be  self-sustaining  as  soon  as  it  begins  to  set. 
Points  to  Consider  in  Design  of  Forms. — The  design  of 
forms  must  take  into  consideration  the  following  points: 

(1)  Cost  of  lumber  and  labor. 

(2)  Size  and  nature  of  the  work;  whether  the  forms  may 
be  used  over  and  over  again,  or  whether  the  lumber  in  the 
forms  should  be  detachable,  so  as  to  be  reapplied  as  the  work 
goes  on. 

(3)  Means  of  supporting  forms,  attention  being  given  to 
initial  stresses  in  reinforcement  erected  in  advance  and  used, 
to  support  the  forms,  such  as  is  the  case  where  steel  skeleton 
structures  are  rapidly  erected,  several  floors  being  concreted 
simultaneously. 

Assumptions  Made  in  the  Design  of  Forms. — The  con- 
struction of  forms  is  considered  as  a  temporary  one;  hence 
the  stresses  allowed  are  more  liberal  than  they  would  be  in 
permanent  constructions.  For  the  design  of  forms  the  fol- 
lowing assumptions  are  made: 

(1)  Concrete  weighs  150  Ibs.  per  cu.  ft. 

(2)  A  live  load  representing  the  weight  of  laborers  with 
wheelbarrows  and  material  is  taken  at  75  Ibs.  per  sq.  ft. 

(3)  For   side   pressure   in   vertical   walls   the  concrete    is 
considered  as  a  liquid  weighing  75  Ibs.  per  cu.  ft. 

(4)  Allowable   compression   in    struts    runs    from   600   to 
1,200  Ibs.  per  sq.  in.,  according  to  the  length  of  the  strut,  and 
for  beams,  750  Ibs.  per  sq.  in.  extreme  transverse  fibre  stress 
is  used. 


194 


REINFORCED    CONCRETE. 


(5)  Deflection  is  calculated  by  the  formula 

n       -5-2^. 

~  384  El 

where  D  ==  greatest  deflection  in  ins. 

W  =  total  load  in  Ibs.  on  plank  or  timber 
L  =  distance  between  supports  in  ins. 
E  =  modulus  of  elasticity  of  lumber 


bh* 


I  =  moment  of  inertia  of  section  of  timber  =  ^77  where 

b  =  breadth,  and 

h  =  depth 

The  value  for  E  may  be  assumed  as  1,300,000  Ibs.  per  sq. 
in.  It  should  be  noted  that  in  a  structure  of  some  height 
where  there  is  a  repetition  of  the  design,  the  falsework  should 
be  used  over  and  over,  in  which  case  the  thickness  of  molds 
is  made  greater  than  strength  and  stiffness  require,  so  as  to 
permit  all  to  be  torn  down  and  reassembled. 


End 
Elevation 


Side    Elevation. 
Fig.  82.— Hennebique  Clamp  for  Girders, 

Fastening  of  Forms. — While  in  the  early  days  of  rein- 
forced concrete,  metal  clamps,  like  the  Hennebique  pattern, 
Fig.  82,  were  much  in  vogue,  modern  practice  prefers  wooden 


BUILDING  DESIGN  AND  CONSTRUCTION.        195 

bracings  with  wedges  as  the  simplest  and  easiest  obtainable 
appliance  for  beams  and  columns.  For  octagonal  columns  a 
very  simple  bracing  is  obtained  by  beveling  the  eight  sides 
of  the  column  so  as  to  fit  together,  bracing  or  squaring  them 
by  means  of  a  wooden  cross  inside,  removable  as  the  con- 
crete progresses,  and  tied  together  every  2  or  3  ft.  vertically 
on  the  outside  by  means  of  No.  18  annealed  wire,  which  is 
loosely  wrapped  a  couple  of  times  around  the  circumference. 
A  %-in.  board  is  inserted  underneath  the  wire  and  twisted 
sidewise  so  as  to  tighten  the  wire,  after  which  a  couple  of 


Fig.  83.— Fastening  for  Octagonal  Column  Mold. 

nails  are  partly  driven  through  the  %-in.  board  into  the  side 
of  the  octagonal  form  as  indicated  by  Fig.  83.  Column-sides 
and  bottom  of  beam-forms  should  be  designed  so  they  may 
be  independent  of  the  slabs.  Washers  should  be  used  on  all 
bolt  heads  and  nuts. 

Joints  in  Forms. — For  dry  concrete  this  is  not  a  matter  of 
great  importance,  but  where  a  wet  mixture  is  used,  poor 
joints  permit  the  escape  of  water  with  cement,  thus  marring 
the  appearance  of  the  finished  work  by  leaving  holes.  Where 
it  is  policy  to  use  a  wet  mixture,  tongued  and  grooved  stuff 


196  REINFORCED    CONCRETE. 

is  considered  advantageous.  All  corners  in  forms  should  be 
filleted,  which  is  generally  done  by  cutting  2x2-in.  stuff  diag- 
onally or  for  round  corners,  by  tacking  1^-in.  hollow  quar- 
ter rounds  in  the  corners. 

Spacing  of  Studs. — As  a  rule  the  spacing  of  studs  for  %-in. 
boards  is  2  ft.;  for  1^-in.  stuff,  3  ft.  6  ins.,  and  for  1^4-in. 
stuff,  4  ft.  6  ins.  The  studs  run  from  2x4  ins.  to  4x6  ins., 
according  to  the  span,  and  4x4  ins.  and  4x6  ins.  are  the  most 
common  dimensions  for  posts.  In  calculating  forms,  par- 
ticular attention  is  paid  to  deflection,  even  more  than  to 
strength. 

Thickness  of  Lagging. — All  material  should  be  dressed  on 
side  and  edge.  The  thickness  varies  from  1/s  in.  to  1$4  ins., 
according  to  circumstances.  The  selection  of  the  stuff  also 
depends  upon  the  method  of  handling,  whether  by  hand  or 
by  derrick.  Sides  for  girders  and  columns  are  generally 
made  of  1^4 -in.  stuff. 

Rotation  in  the  Use  of  Forms. — From  an  economical 
standpoint  great  care  should  be  exercised  in  the  rotation  or 
sequence  in  the  removal  of  falsework  and  forms.  The  fore- 
man should  decide  as  to  the  next  use  or  location  of  his  false- 
work as  well  as  his  forms  and  remember  that  what  he  takes 
down  first  he  will  probably  need  first  in  the  next  location; 
hence  he  should  not  pile  a  lot  of  beam  and  slab  forms  on 
top  of  his  falsework,  but  so  distribute  the  same  that  it  may 
be  accessible.  Forms  should  be  erected  in  such  sequence  as 
to  allow  the  contractor  to  lay  out  his  work  so  as  to  reduce 
the  walking  over  and  on  setting  concrete,  to  a  minimum. 
This  is  an  important  caution  and  by  rights  is  worthy  of  being 
placed  on  a  large  sign  on  every  job. 

Alignment  and  Setting  of  Forms. — Formr,  are  handled 
either  by  hand  or  by  derrick,  and  of  course  should  be  de- 
signed accordingly.  One  point  in  setting  forms  and  false- 
work is  of  the  greatest  importance  and  that  is  to  see  that 
all  verticals  are  absolutely  plumb  and  maintained  plumb. 
Not  only  the  foreman  but  every  man  on  the  job  should  be 
on  the  watchout  for  alignment  in  both  directions. 


BUILDING  DESIGN  AND  CONSTRUCTION.         197 

During  the  depositing  of  the  concrete  the  author  has 
made  it  a  practice  to  have  two  good  carpenters  do  nothing 
but  watch  the  alignment  of  the  forms  for  columns,  girders, 
beams  and  slabs  by  driving  and  setting  the  wedges  or  placing 
such  shims  inside  the  column  braces  as  may  be  required. 
As  the  molds  will  have  more  or  less  of  a  sag  after  being 
filled  with  concrete,  it  is  customary  to  give  them  a  slight 
camber  so  as  to  make  them  absolutely  horizontal  when  the 
concrete  is  hardened.  The  wedges,  as  a  general  rule,  should 
be  sharp  and  thin  enough  to  stick  without  being  tacked  and 
the  pride  of  every  foreman  should  be  to  have  his  forms 
removable  and  collapsible  so  as  to  be  compelled  to  pull  as 
few  nails  as  possible  in  shifting. 

Adhesion  of  Concrete  to  Forms. — To  prevent  adhesion  of 
concrete  to  the  forms,  a  coat  of  crude  oil  or  soft  soap  and 
water  is  considered  the  most  practicable,  but  if  the  forms 
are  to  be  left  on  until  the  concrete  is  hard,  there  is  little 
danger  of  the  concrete  sticking  to  them,  if  they  are  thor- 
oughly wet  with  water  before  the  concrete  is  laid. 

After  removing  the  forms  they  should  be  brushed  thor- 
oughly with  a  stiff  brush  to  remove  all  loose  material,  at 
any  rate  while  the  forms  are  new.  It  is  found  that  crude  oil 
need  be  applied  but  once  or  twice,  as  it  seems  the  pores  of 
the  wood  are  filled  thereby,  and  also  by  cement,  which  pre- 
vents old  forms  from  sticking  to  the  concrete.  The  careful 
cleaning  of  forms  is  essential  if  a  smooth,  firm  face  is  desired. 

Time  to  Remove  Forms. — This  is  a  matter  of  great  im- 
portance, and  lack  of  attention  to  this  item  has  caused  most 
of  the  disastrous  accidents  to  reinforced  concrete.  The  time 
for  removal  depends  on  the  following  considerations: 

(1) — The  consistency  of  the  concrete,  whether  wet  or  dry. 

(2) — The  quantity  of  concrete  in  the  members  considered. 

(3) — The  temperature. 

(4)— The  humidity  of  the  air. 

As  a  fair  example,  it  may  be  suggested  that  for  walls  in 
mass  work,  one  to  three  days  should  be  allowed,  or  until  the 
concrete  will  bear  the  pressure  of  the  thumb  without  indenta- 


198 


REINFORCED    CONCRETE. 


tion.  For  thin  walls  in  summer,  two  days,  in  cool  weather 
five  days;  slabs  in  summer  six  days,  in  cool  weather  two 
weeks.  Beams  and  girders  in  long-span  slabs  in  summer 
ten  days  or  two  weeks,  in  cool  weather  three  weeks  to  one 
month.  Column  forms  in  summer  four  days,  in  winter  six 
days,  providing  the  girders  are  shored  up  to  prevent  appre- 
ciable weight  on  the  columns.  Arches  of  small  size  one 
week,  large  arches  with  heavy  dead  load  one  month.  These 


Fig.  84.— Arrangement  of  Studding  and  Lagging  to  Provide  for 
Swelling. 

are  but  suggestions,  as  the  removal  of  forms  should  be  left 
entirely  to  the  judgment  of  the  experienced  engineer  in 
charge. 

For  face  work,  arrangement  should  be  made  so  the  molds 
can  be  withdrawn  without  tearing  the  corners  of  ornaments. 

Mr.  Douglas*  uses  a  method  indicated  by  Fig.  84,  where 

*  Engineering  News,  Jan.  24,  1907. 


BUILDING  DESIGN  AND  CONSTRUCTION. 


199 


he  provides  a  loose  strip  of  lagging  at  B,  so  it  can  be  pulled 
back  to  a  recess  in  the  stud  after  6  to  12  hours  to  allow  for 
shrinkage  of  concrete  and  swelling  of  forms. 

An  exaggerated  illustration  of  the  effect  of  the  swelling  of 
lagging  on  continuous  studding  is  shown  at  II,  Fig.  84. 


f*-/6 


Pig.  85. — Forms  for  Girders,  Beams,  Slabs  and  Columns. 

Column  and  Floor  Forms. — Numerous  constructions  of 
column  and  floor  forms  are  used.  The  construction  shown 
by  Fig.  85  is  a  representative  example.  This  form  was 
designed  by  Mr.  R.  A.  Cummings. 

Forms  in  Combined  Steel  and  Concrete  Construction. — 
Where  concrete  floors  rest  on  structural  steel  or  where  struc- 
tar?l  steel  is  erected  first,  as  a  skeleton  and  the  members  so 


200  REINFORCED    CONCRETE. 

located  as  to  form  the  tension  part  of  the  reinforced  con- 
crete construction,  the  forms  should  be  supported  on  the 
temporary  steel  beams  and  girders  so  as  to  give  them  a  cer- 
tain stress  during  the  placing  of  the  concrete,  which  other- 
wise would  act  as  an  initial  stress  in  the  steel,  if  the  false- 
work were  supported  from  below. 

Separately  Molded  Members. — For  some  time  in  Europe, 
and  recently  in  this  country,  attention  has  been  turned  to  the 
possibility  of  a  building  construction  of  columns,  girders  and 
slabs  molded  separately  and  erected  similarly  to  steel  or  tim- 
ber construction.  Whatever  may  be  said  in  other  respects 
of  this  type  of  construction  in  comparison  with  monolithic 
construction  in  place,  it  certainly  has  the  advantage  of  re- 
ducing the  cost  of  form  work.  Thus  several  one-story  ware- 
houses built  for  the  Bush  Terminal  Co.  of  Brooklyn  have 
reinforced  concrete  columns,  girders  and  roof  slabs  cast  on  the 
ground  and  then  erected.  Mr.  Goodrich,  the  designer,  de- 
scribes the  work  substantially  as  follows:  "For  molds  for 
columns  cast  on  one  side,  only  three  pieces  were  needed  in 
place  of  four.  This  effects  a  saving  of  25  per  cent  in  ma- 
terials for  molds,  besides  doing  away  with  clamps,  bolts  and 
braces.  Another  advantage  obtained  by  these  column  forms, 
shared  also  by  girder-forms,  was  that  the  side  boards  could 
be  removed  after  24  or  at  the  most  48  hours  and  used  again 
two  or  three  times  during  the  interval,  while  they  must  have 
been  left  in  place  if  the  molding  had  been  done  in  place. 
This  alone  saves  SO  per  cent  in  materials  for  forms,  as  only 
the  narrow  bottom  boards  were  needed  in  any  great  numbers. 
A  much  greater  saving  was  made  in  the  centers  for  the  roof 
slabs.  The  concrete  ground  floor  was  laid  as  soon  as  the 
columns  and  girders  had  been  erected.  On  this  flat  surface 
ordinary  building  paper  was  spread  and  the  roof  slabs  marked 
out  by  narrow  strips  of  wood  of  a  height  just  equal  to  the 
desired  thickness  of  the  slab.  The  reinforcing  rods  were 
then  placed  and  the  concrete  deposited." 

Frames  and  trims  for  partition  and  wall  openings  are  sep- 
arately molded  in  permanent  galvanized  iron  forms,  as  shown 


BUILDING  DESIGN  AND  CONSTRUCTION. 


201 


in  Fig.  86,  and  this  method  entirely  does  away  with  the  com- 
bustible wooden  trim  usually  employed  in  building  construc- 
tion. 

Eliminating  the  Use  of  Forms. — Inasmuch  as  forms  rep- 
resent more  or  less  waste  of  material,  considerable  attention 
has  been  given  to  reinforced  concrete  construction  in  .which 
forms  are  reduced  to  a  minimum.  Thus  in  constructing  the 
interior  columns  of  a  factory  building  erected  by  the  Bush 
Terminal  Co.  of  Brooklyn  cylindrical  forms  of  cinder  con- 
crete \l/2  ins.  thick  cast  in  proper  molds  were  set  end  on  end 
to  the  proper  height  to  form  a  mold  for  the  column  concrete. 


rrte... 


Ceiling  r> 


Section  of  Door  Frame 
Tile  Partition. 


Section  of  Base  Boards 
•for  "Tile  Partition. 


Section  of  Bass  Boards 

and  Cap-for  Picture  Mould 

at  Celling. 


Fig.  86.— Separately  Molded  Details  for  Doors,  Windows  and 
Partitions. 


Spiral  reinforcement  was  adopted  for  the  columns  and  was 
molded  into  the  shell,  so  that  the  placing  of  the  column  form 
also  placed  the  column  reinforcement.  There  was  gained  at 
once  by  this  scheme  of  form  work,  a  fireproofing  for  the  col- 
umn, the  placing  of  the  form  and  reinforcement  in  one  opera- 
tion by  unskilled  laborers  and  the  elimination  of  labor  for  re- 
moval of  forms.  As  for  the  shells  themselves,  their  cost  was 
certainly  not  greater  and  was  probably  less  than  would  have 
been  for  cylindrical  molds  in  wood. 

In  the  Wiederholdt  system  of   reinforced   concrete   con- 
struction, no  forms  whatever  are  used.      Fig.  87  shows  the 


202 


REINFORCED    CONCRETE. 


system  as  applied  to  wall  construction.  By  the  use  of  hollow 
tile  blocks  of  special  shape,  thin  shells  of  fire  clay  or  cement 
tile  are  used  as  molds  and  form  the  exterior  surface.  The 
vertical  steel  bars  are  embedded  in  the  foundation  in  the 
usual  way,  and  the  tiles  are  laid  between  them  with  horizontal 
bars  at  suitable  intervals,  after  which  the  concrete  is  placed, 
the  tiling  and  concrete  being  carried  up  as  the  work  pro- 
gresses. This  system  is  also  adapted  to  the  construction  of 
grain  and  other  storage  buildings,  and  especially  for  smoke 
stacks. 

Small  Tools  for  Mixing,  Conveying  and  Ramming. — As 
reinforced  concrete  construction  has  developed,  the  tools  used 
have  changed  considerably.  They  are  becoming  standardized 
as  the  importance  of  this  phase  of  the  work  is  being  recog- 


Vert.&Hor.Rods  i' 
Bars  -to  Lap  Zat 


Fig.  87.— Wall  Construction,  Wiederholdt  System. 

nized.  While  formerly  the  same  tools  that  were  used  for 
brick  and  mortar  were  used  for  concrete  work,  now  special 
tools,  adapted  to  the  peculiarities  of  concrete  work,  are  a 
great  advantage. 

Instead  of  the  old-fashioned  wooden  brick  and  mortar 
barrows  formerly  in  use/  most  contractors  are  now  using 
iron  wheel  barrows,  Fig.  88,  or,  for  larger  work,  a  Ransome 
concrete  cart,  Fig.  89.  The  latter  is  built  entirely  of  steel, 
and  as  it  has  large  wheels  is  very  easy  to  move  about,  en- 
abling one  man  to  move  several  times  as  much  material  as 
he  can  handle  with  a  wheel  barrow.  This  form  of  cart  is 
easy  to  dump  and  the  concrete  is  not  readily  spilled  over  the 
side  of  the  bowl.  This  saves  time  and  material.  It  is  stated 


BUILDING  DESIGN  AND  CONSTRUCTION. 


203 


by  the  manufacturers  that  the  cost  of  moving  concrete  with 
an  iron  push  cart  is  \1/^  cts.  per  cu.  yd.  per  100  ft.  of  haul. 

Square  pointed  shovels  are  generally  employed  and  for 
mixing  and  handling  the  materials  size  No.  3  is  considered 
the  best. 


Fig.  88. — Iron  Wheelbarrow  for 
Handling  Concrete. 


Fig. 


j. — Ransome    Concrete 
Cart. 


A  simple  measuring  box  is  shown  by  Fig.  90.  It  is  bot- 
tomless and  8  to  10  ins.  high,  and  of  a  size  to  suit  the  mix- 
ture. Thus,  if  in  a  1-6  mixture  the  proportions  1-2-4  give 


Fig. 


90. — Measuring   Box   for 
Aggregates. 


Fig.  91.— Cast  Iron  Rammer 
for  Dry  Concrete. 


the  greatest  density,  the  box  would  be  8  ins.  deep  and  2  ft. 
7l/2  ins.  x4  ft.  This  box  should  be  filled  once  with  sand  and 
twice  with  broken  stone,  each  time  being  struck  off  level 


204  REINFORCED    CONCRETE. 

Sometimes  hoes  are  used  for  mixing  material  and  give 
good  results,  particularly  if  one  of  the  men  is  a  regular  mor- 
tar mixer. 

Rammers  are  used  for  compacting  the  materials.  For 
dry  mixtures  a  flat  rammer,  usually  cast  iron  with  7x7  ins. 
base,  as  shown  by  Fig.  91,  is  used.  These  generally  weigh 
from  6  to  8  Ibs.,  while  for  wet  concrete  a  wooden  rammer, 
Fig.  92,  is  used  to  cut  and  compact  the  material.  For  thin 
walls  a  tool  having  a  long  flat  steel  plate  mounted  on  a 
handle  will  be  found  of  use.  For  large  work  pneumatic  ram- 
mers built  on  the  principle  of  pneumatic  riveting  machines 
have  been  used.  Other  tools,  such  as  mixers  and  crushers, 
have  been  referred  to  before  and  the  different  contracting 
equipment  companies  issue  very  complete  catalogs  from 
which  selections  can  be  made. 


Fig.   92.— Wooden  Rammer  for  Wet  Concrete. 

FINISHING  CONCRETE  SURFACES. 

Since  the  character  of  a  concrete  structure  is  judged 
largely  by  the  appearance  of  the  exterior,  the  finishing  of 
such  surfaces  becomes  very  important.  In  the  first  place, 
concrete  is  a  comparatively  new  building  material,  different 
from  iron,  wood,  or  tile,  and  should  be  recognized  as  such 
by  giving  it  a  distinct  concrete  appearance.  To  the  author's 
mind,  imitation  of  other  materials  is  out  of  place  in  concrete 
structures.  The  manner  of  finishing  must  be  governed  by 
the  size  and  class  of  the  structure  and  the  style  of  architec- 
tural decoration.  The  facility  with  which  concrete  lends 
itself  to  ornamentation  enables  the  choice  of  a  style  of  ar- 
chitecture with  features  that  otherwise  might  be  considered 
very  expensive.  On  the  whole,  simplicity  and  plainness  in 
general  outlines  should  mark  concrete  construction. 


BUILDING  DESIGN  AND  CONSTRUCTION.         205 

Types  of  Finish. — There  are  five  main  types  of  finish  for 
concrete: 

(1)  Leaving  the  concrete  as  it  is  when  the  forms  are  re- 
moved. 

(2)  Hammer  dressing  or  tooling. 

(3)  Using  a  mortar  facing  or  plastering. 

(4)  Using  special  concrete  mixtures. 

(5)  Washing  away  the  cement  to  expose  the  aggregates. 
Hair  Cracks. — Smooth  concrete  surfaces  often  show  cracks 

generally  caused  by  using  a  wet  concrete,  in  which  the  ex- 
cess of  water  carries  to  the  surface  and  deposits  a  coating 
of  very  fine  cement  which  sets  and  contracts  at  a  different 
rate  from  the  underlying  concrete.  These  cracks  can  be 
eliminated  by  covering  the  concrete  with  wet  sand  or  saw- 
dust, which  is  kept  well  sprinkled  for  some  time  after  the 
placing  of  the  concrete.  Too  rich  a  mixture,  or  a  surface 
mixture  richer  than  the  body  concrete,  will  also  cause  hair 
cracks.  If  impracticable  to  cover  with  sawdust,  the  surface 
showing  cracks  may  be  scrubbed  thoroughly  with  a  wire 
brush  or  a  cement  brick  to  remove  the  cement  film. 

Mortar  Facing. — To  produce  a  smooth  surface  finish  on 
concrete  a  mortar  facing  is  often  used,  varying  in  thickness 
from  1  in.  to  3  ins.  To  place  this  facing  a  steel  plate  is  in- 
serted in  the  form  and  held  away  from  it  by  means  of  angle 
irons  from  1  in.  to  \l/2  ins.  wide,  depending  upon  the  thick- 
ness of  facing  required.  The  concrete  is  put  into  the  form 
back  of  the  plate  and  the  mortar  into  the  narrow  space  be- 
tween the  form  and  the  plate,  and  the  plate  is  carefully  with- 
drawn. 

Another  method  of  obtaining  a  smooth  surface  is  to  use 
a  very  wet  concrete  and  throw  it  violently  against  the  mold, 
so  that  the  aggregates  rebound  leaving  in  effect  a  mortar 
facing.  This  is,  however,  not  to  be  recommended  for  fine 
work,  as  the  molds  are  apt  to  be  indented  and  the  alignment 
impaired. 


206  REINFORCED    CONCRETE. 

Using  Special  Dry  Mixture. — This  method  has  been  used 
extensively  for  park  buildings  in  Chicago  and  is  described 
by  Mr.  Linn  White  as  follows: 

"The  method  consists  in  using  for  the  exposed  surfaces 
the  walls  of  concrete  composed  of  one  part  of  cement  and 
three  parts  of  fine  limestone  screenings  and  three  parts  of 
crushed  limestone  known  as  the  ^-in.  size.  This  was  then 
mixed  quite  dry,  so  no  mortar  was  flushed  to  the  surface, 
and  well  rammed  in  wooden  forms.  It  was  not  spaded  next 
the  form,  and  was  too  dry  to  cause  any  flushing  of  mortar. 
The  imprints  of  joints  between  the  boards  were  hardly  no- 
ticed, and  no  efflorescence  can  appear  on  the  surface  on  ac- 
count of  the  dryness  of  the  mix  and  the  porosity  of  the  sur- 
face. The  same  finis'h  has  been  successfully  used  for  retain- 
ing walls,  arch  bridges,  fence  posts,  walls  enclosing  service 
yards,  etc.  A  dry,  rich  mix  with  finely  crushed  stone  has 
been  found  especially  suited  to  another  condition  where  a 
sound,  smooth  surface  was  particularly  difficult  to  secure, 
namely,  for  the  under-water  portion  of  a  sea  wall  on  Lake 
Michigan.  It  was  mixed  very  dry  and  dumped  in  sunken 
boxes,  joined  end  to  end,  made  fairly  water-tight,  but  from 
which  water  was  not  excluded.  With  a  finely  crushed  stone, 
a  sound,  smooth  surface  was  obtained  when  the  sides  of  the 
boxes  were  removed  where  it  was  manifestly  impossible  to 
plaster  or  grout  the  surface  and  where  spading  a  mix  of 
coarser  stone  would  obviously  wash  away  the  cement." 

Bringing  Aggregates  Into  Relief. — This  gives  a  finish 
which,  to  the  author's  mind,  is  superior  to  a  smooth  surface, 
since  with  it  variations  in  color,  efflorescence,  hair  cracks, 
and  other  superficial  blemishes  are  practically  removed.  The 
simplest  method  of  bringing  out  this  rough  effect  is  to  scrub 
the  concrete  with  brushes  while  it  is  green,  as  soon  as  the 
forms  are  removed.  In  cases  where  the  forms  must  be  left 
until  concrete  is  hard,  the  cement  may  be  removed  by  the 
application  of  a  weak  acid  solution,  which  afterwards  should 
be  neutralized  with  an  alkaline  solution  and  then  well  washed 
with  water.  Rubbing  with  a  small  block  of  wood  or  sand- 


BUILDING  DESIGN  AND  CONSTRUCTION.        207 

stone  or  scrubbing  with  a  stiff  wire  brush  also  removes  a 
hard  cement  coating.  When  the  forms  are  removed  at  the 
right  time,  three  or  four  passages  of  an  ordinary  scrubbing 
brush  with  plenty  of  water  is  all  that  is  required  and  a  la- 
borer can  wash  about  100  sq.  ft.  in  an  hour  where  the  work  is 
easily  accessible. 

Tooling. — Tooled  surfaces  are  obtained  on  concrete  simi- 
larly as  for  stone.  When  the  concrete  is  hardened,  the  sur- 
face may  be  bush-hammered  or  treated  in  any  other  man- 
ner. In  these  cases  the  forms  may  be  of  rough  lumber. 
Tooling  the  surface  generally  costs  from  3  to  10  cts.  per  sq. 
ft.,  according  to  quantity  and  outfit.  The  Citizens'  National 
Bank  of  Los  Angeles,  Cal.,  was  finished  with  bush-hammer- 
ing at  a  cost  of  ll/2  cts.  per  sq.  ft.,  common  laborers  at  $2  a 
day  doing  the  work. 

Plastering  Concrete. — When  plaster  is  to  be  applied  to 
concrete  the  concrete  should  be  left  quite  rough,  so  as  to 
form  a  clinch.  There  should  be  no  difficulty  in  causing  the 
layers  to  adhere  to  each  other  if  properly  applied.  The  con- 
crete should  be  well  sprinkled  before  the  plaster  is  laid,  as 
the  interior  concrete,  being  dry,  will  otherwise  absorb  moist- 
ure and  prevent  adhesion.  In  every  case  the  plaster  must 
be  rubbed  and  tooled  hard  against  the  concrete,  and  while 
surfacing  more  water  should  be  applied  by  means  of  a  sprink- 
ling brush. 

Painting  and  Varnishing. — Cement  floors  can  be  -painted 
and  varnished  like  wood  if  first  the  surface  is  primed  with  a 
solution  that  will  fill  the  pores  and  stop  capillary  action.  A 
solution  of  hydrofluoric  acid  has  been  used  for  this  purpose 
to  good  advantage. 

WATERPROOFING. 

With  the  increased  use  of  concrete  and  reinforced  con- 
crete, waterproofing  is  daily  becoming  of  greater  importance. 
A  number  of  patented  preparations  have  been  invented  and 
put  on  the  market  to  serve  the  purpose  of  making  a  struc 
tnre  waterproof,  either  by  application  on  the  outside  of  the 
wall  or  on  the  inside,  and  in  some  instances  by  adding  chem- 


208  REINFORCED    CONCRETE. 

ical  substances  to  the  cement,  so  as  to  form  a  gelatinous  sub- 
stance, which  prevents  the  absorption  of  water  and  still  have 
no  harmful  effect  on  the  crystallizing  of  the  cement.  In  the 
author's  opinion,  waterproofing  is  as  yet  in  its  infancy,  and 
owing  to  the  increasing  demand,  great  attention  is  now  being 
given  to  the  matter  by  chemists  and  waterproofing  engineers. 
At  present  we  must  realize  that  the  simplest  means  of  re- 
ducing permeability  in  concrete  is  to  increase  its  density, 
both  in  the  selection  and  application  of  aggregates  and  in 
compressing  the  surface  after  finishing  by  vigorous  tooling 
or  rubbing.  Impurities  in  water  through  seepage  assist  in 
making  tanks  water-tight  by  filling  the  pores,  and  numerous 
tanks  and  pipes  have  been  made  water-tight  without  the  ad- 
dition of  any  particular  preparation  to  the  material  or  on  the 
surface.  When,  however,  we  notice  the  leaking  or  dripping 
from  subways,  tunnels,  or  concrete  coverings,  or  suffer  from 
wet  or  damp  cellars  or  basements,  we  must  realize  that  lack 
of  proper  waterproofing  is  a  menace  to  public  health.  To 
reduce  the  personal  equation  to  a  minimum  it  is  the  safest 
to  apply  a  waterproofing  layer  of  felt,  tar,  asphalt  or  pitch, 
as  the  case  may  be,  and  where  it  will  do  the  most  good.  In- 
asmuch as  waterproofing  is  a  specialty  and  requires  skilled 
mechanics  for  its  proper  application,  and,  furthermore,  in- 
asmuch as  the  different  waterproofing  companies  generally 
provide  their  own  waterproofing  compounds,  it  is  hardly 
within  the  province  of  this  book  to  go  further  into  details 
than  to  offer  the  following  advice  in  the  specifications: 

(1)  Design  the  structure  so  as  not  to  make  application 
of  waterproofing  impossible  for  lack   of  space   of   operation. 

(2)  No  waterproofing  must  be  done  under  a  lower  tem- 
perature than  25°  F. 

(3)  Waterproofing   must    be    done    only   by    experienced 
and  skilled  laborers. 

(4)  Watch    the   waterproofing   during   and   after   the    ap- 
plication, and  inspect  the  work  during  progress. 

(5)  Do  not  depend  upon  guarantees. 

(6)  Do  not  stick  to   a   standard   specification,   but   make 
a  specification  to  suit  local  circumstances. 


BUILDING  DESIGN  AND  CONSTRUCTION.        209 

Waterproofing  Cracked  Walks  or  Joints  Between  Steel 
and  Concrete. — Here  an  elastic  putty  is  required — and  the 
author  after  much  experimenting  finally  obtained  satisfactory 
results  as  follows: 

1.  With  a  cold  chisel  cut  a  groove  2  ins.  to  2l/2  ins.  deep,  ^ 
in.  wide,  along  the   crack  or  adjoining  the   steel. 

2.  Tightly  caulk  one-half  this  depth  with  oakum. 

3.  Paint  the  top  of  oakum  and  the  sides  of  groove  above 
oakum  with  No.   110  R.  I.  W.    (a  preparation  manufactured 
by  Toch  Bros.,  520  Fifth  Ave.,  New  York  City). 

4.  Make  a  putty  by  kneading  one-half  volume  dry  Port- 
land  cement  with  one-half  volume   No.    110  R.   I.   W.  until 
the  putty  does  not  stick  to  the  hand. 

5.  Stuff  this  putty  in  on  top  of  the  oakum,  entirely  filling 
the  groove  and  sprinkle  dry  cement  on  top  of  finished  joint. 

6.  Absolutely   no   water   must  be  used  and  the  grooves 
must  be  dry. 

Experiments  indicate  that  concrete  can  also  be  'rendered 
impervious  to  water  through  the  addition  of  at  least  5  per 
cent — and  not  more  than  10  per  cent — of  the  weight  of 
cement  of  petroleum  residuum  oil,  without  impairing  the 
strength  of  the  concrete. 

Oil-mixed  mortar  containing  10  per  cent  of  oil  is  abso- 
lutely watertight  under  pressure  as  high  as  40  Ibs.  per 
sq.  in.  Such  mortar  may  also  effectively  be  painted  or 
plastered  on  either  side  of  porous  concrete. 

The  crushing  strength  of  concrete  with  oil  is  reduced  to 
75  per  cent  at  28  days,  but  1  :  3  mortar  suffers  practically  no 
harm  at  the  age  of  one  year. 

(L.  W.  Page.    Proc.  Am.  Soc.  C.  E.,  Vol.  XXXVII,  p.  994.) 

Protection  of  Steel  Which  Is  to  Be  Incased  in  Concrete. — 
Usually  reinforcements  are  not  painted  but  structural  steel, 
which  may  remain  exposed  in  shop,  transit  or  during  erec- 
tion previous  to  being  incased  in  concrete,  should  have  a 
shop  coat  of  a  cement  paint,  such  as  Tockolith,  manufactured 
by  Toch  Bros,  of  520  Fifth  Ave.,  New  York,  and,  if  delayed 
in  erection,  a  second  coat  of  the  same  material  will  effectively 


210 


REINFORCED    CONCRETE. 


protect   the   steel  without   injuring   its   adhesion   to   the   con- 
crete. 

Toxement. — Two  pounds  of  Toxement  (Toch  Bros.,  New 
York),  added  to  each  bag  of  Portland  cement  used  in  the 
concrete  will  make  the  latter  impervious  to  water.  This  mixture 
has  proved  very  satisfactory  in  all  instances  which  have  come 
under  the  author's  personal  supervision. 


TABLE    LIX-A. — COLORING  OF  CEMENT  MORTAR. 
1  part  of  Portland  cement  to  2  parts  sand. 


Weight  of  Dry  Coloring  Matter  to  100  Lbs.  Cement. 

•P 

Dry 

"o  £ 

Material 

2  ^ 

Used. 

*o  S;    • 

Yi  lb. 

lib. 

21bs. 

41bs. 

J^ls  g 

So 

Lampblack 

Light  Slate 

Light  Gray 

Blue  Gray 

Dark  Blue 

15 

t 

Slate 

Prussian  Blue 

Light  Green 

Light  Blue 

Blue  Slate 

Bright  Blue 

50 

Slate 

Slate 

Slate 

Ultramarine  Blue 

Light  Bluf 

Blue  Slate 

Bright  Blue 

20 

Slate 

Slate 

Yellow  Ocher 

Light  Green 

Pinkish  Slite 

Light  Buff 

3 

Burnt  Umber 

Light  Pinkish 
Slate 

Dull  Lavender 
Pink 

Chocolate 

10 

Venetian  Red 

Slate,  Pink 

Bright  Pinkish 

Light  Dull 

Dull  Pink 

2J^ 

Chattanooga  Iron 

Tinge 
Light  Pinkish 

Slate 
Dull  Pink 

Pink 
Light  Terra 

Light  Brick 

2 

Ore 

Slate 

Cotta 

Red 

Red  Iron  Ore 

Pinkish  Slate 

Dull  Pink 

Terra  Cotta 

Light  Brick 
Red 

2H 

CHAPTER  III. 
THE    DESIGN   AND    CONSTRUCTION    OF    BRIDGES. 

The  methods  employed  in  bridge  construction  vary  with 
the  design  and  the  type  of  the  bridge. 

Bridges  are  classified  as  Flat  Slab,  Girder  Spans  and  Arches. 

The  two  first  classes  are  similar  in  design  to  floor  slabs 
and  girders  for  buildings  and  are  used  for  short  spans  and 
light  traffic. 

FLAT  SLAB  AND  GIRDER  BRIDGES. 

(After  "Designing  Methods,"  by  Lindau.) 
A  flat  slab  design  will  in  general  be  found  more  desirable 
and  economical  for  spans  up  to  twenty  feet;  for  longer  spans 
a  girder  type  bridge  should  be  used.  By  a  "girder  bridge" 
is  meant  a  comparatively  thin  reinforced  concrete  decking 
carried  by  girders  extending  from  abutment  to  abutment; 
these  girders  should  preferably  be  entirely  below  the  deck- 
ing. In  some  cases,  however,  the  side  girders  may  be  carried 
up  above  the  slab  to  form  the  side  rail.  Girder  bridges  are 
economical  under  the  usual  conditions  for  spans  of  from 
eighteen  to  thirty-five  feet;  for  longer  spans  an  arch  bridge 
will  probably  be  more  desirable.  Girder  bridges  have  been 
built  for  spans  as  great  as  sixty  or  seventy  feet;  these  larger 
structures,  however,  should  be  specially  designed,  and  we 
have  made  no  attempt  to  include  such  unusual  structures  in 
the  standard  tables  given. 

CLASSIFICATION   BY   LOADINGS. 

Highway  bridges  must  be  designed  to  safely  carry  the 
heaviest  load  likely  to  come  upon  them,  and  as  this  maximum 
load  varies  with  the  locality  we  have  arbitrarily  adopted  three 
standard  classifications  by  loadings,  which  should  cover  all 
usual  conditions. 

211 


212 


REINFORCED    CONCRETE. 


In  short  span  bridges,  such  as  we  are  now  considering, 
the  concentrated  loads  are  the  determining  factors  in  the 
design — the  uniformly  distributed  loads  usually  specified  (100 
to  150  pounds  per  square  foot)  causing  smaller  stresses. 

Class  No.  1. — Light  highway  specification  answering  the 
purposes  of  ordinary  country  traffic  where  the  heaviest  load 
may  be  taken  as  a  12-ton  road  roller.  Uniformly  distributing 
load,  100  pounds  per  square  foot. 

Class  No.  2. — Heavy  highway  specification,  designed  for 
localities  where  heavy  road  rollers,  up  to  20  tons,  and  electric 
cars  of  a  maximum  weight  of  40  tons  must  be  provided  for. 
Uniformly  distributed  load,  125  pounds  per  square  foot. 

Class  No.  3. — City  highway  specification,  designed  for 
heavy  concentrated  loads  and  large  interurban  cars.  This 
classification  should  be  adopted  for  all  city  work;  the  weight 
of  the  maximum  car  has  been  taken  as  60  tons.  Uniformly 
distributed  load,  150  pounds  per  square  foot. 


LOAD  DIAGRAMS. 

The  following  diagrams  represent  the  loadings  adopted  in 
the  above  classifications  and  used  in  the  design  of  the  cul- 
verts and  bridges  shown  herein: 


.47-0'- 


-8'6- 


71?      ..     W 

H 24-0"— Ul 

fcSfc*  kftTJ 


Fig.  92-A. — Standard  Car,  Class  No.  2 — 40  tons  on  eight  wheels. 


BRIDGE  DESIGN  AND  CONSTRUCTION.  213 


Fig.  92-B. — Standard  Car,  Class  No.  3 — 60  tons  on  eight  wheels. 


The  concentrations  due  to  a  steam  roller  will  be  taken  as 
indicated  by  Fig.  92-C;  two-thirds  of  the  total  load  being  as- 
sumed on  the  rear  wheels. 


/t-O 


o 


Fig.    92-C. — Road   Roller   Loading   Diagram,    Class   2. 


Note. — Reinforced  concrete  slab  bridges  are  very  stiff  and 
that  part  of  the  slab  directly  under  the  concentrated  load  is 
materially  assisted  by  the  adjoining  sections.  To  assist  this 
lateral  distribution  of  load  transverse  reinforcement  should 
be  used  in  all  slab  bridges. 


214 


REINFORCED    CONCRETE. 


LIVE    LOADS. 

A  uniformly  distributed  load  shall  be  considered  as  caus- 
ing the  specified  pressure  per  square  foot  on  the  bridge  re- 
gardless of  depth  of  fill. 

A  minimum  fill  of  twelve  inches  is  required  on  all  bridges. 

Wheel  or  road  roller  concentrations  shall  be  considered 
as  acting  on  a  line  whose  length  equals  the  out  to  out  tread 
of  the  wheels. 

Loads  on  car  tracks  shall  be  considered  as  uniformly  dis- 
tributed over  a  width  of  roadway  equal  to  the  length  of  the 
ties  and  in  the  direction  of  the  track  for  a  distance  of  two 
feet  on  both  sides  of  single  wheels  and  for  a  distance  of  the 
wheel  base  plus  two  feet  for  trucks. 

The  above  distribution  of  load  is  at  the  level  of  the  road- 
way. The  following  methods  of  findiag  the  loads  on  the 
bridge  itself  are.  suggested: 

Wheel  Loads  on  Roadway. — Assume  distribution  of  load 
by  fill  to  be  only  in  the  direction  of  the  roadway  and  to  be 
carried  down  on  a  slope  of  l/2  to  1.  The  following  diagram, 
Fig.  92-D,  showing  the  distribution  of  road  roller  concentrations, 

illustrates  our  method. 


—  //-O' 


Fig.    92-D. — Showing  Distribution   of 
Loads  Due  to  Road   Roller. 


With  this  arbitrary 
distribution  of  loading 
it  will  be  noted  that  for 
a  strip,  the  width  of  the 
front  wheel,  the  loaded 
areas  overlap  when  the 
depth  of  fill  is  greater 
than  the  distance  be- 
tween axles.  In  this 
case,  consider  the  load 
as.  uniformly  distributed 
over  an  area  of  slab  7'6" 
wide  by  (d+ll'O")  long. 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


215 


Wheel  Loads  on  Tracks. — See  distribution  by  track  sys- 
tem, page  211.  These  loads  will  be  considered  as  distributed 
in  a  manner  similar  to  that  adopted  for  wheel, loads  on  the 
roadway,  excepting  that  the  distribution  will  be  assumed 
to  be  in  both  directions.  It  should,  however,  be  borne  in 
mind  that  on  double  track  slab  bridges  the  width  of  slab 
considered  as  supporting  one  track  can  not  be  taken  as 
greater  than  the  distance  c.  to  c.  of  tracks. 

Impact.— When  the  fill  is  less  than  five  feet  add  25% 
for  impact  for  rapidly  moving  loads. 

The  following  diagram  (Fig.  92-E)  shows  the  assumed  dis- 
tribution of  standard  truck  load,  40- ton  car. 


«"*--"<"<-l£  ••••  ~"~'fam,w,.m,>*™>iJr" 

'UJ\      >>        /l-»*-tfJ\ 


r,*  L*»fffc 


Fig.   92-E. — Load  Distribution,  40-Ton  Car. 


Treatment  of  Loads  for  Girder  Bridges. — The  distribu- 
tion of  loads  through  the  fill  will  be  as  above  outlined;  in 
this  type  of  bridge,  however,  the  girders  must  be  so  located 
as  to  properly  take  care  of  the  track  loads.  The  girders 
under  the  tracks  being  assumed  to  carry  the  full  load. 

Abutments  and  Side  Walls.— For  the  design  of  abutments 
and  side  walls  take  the  horizontal  component  of  the  earth 
pressure  as  one-third  of  the  vertical  pressure  at  that  depth, 
assuming  the  resultant  to  act  at  a  distance  one-third  the 


216  REINFORCED    CONCRETE. 

height  above  the  base.  The  intensity  of  the  horizontal  pres- 
sure due  to  live  load  may  also  be  taken  equal  to  one-third 
of  the  vertical  intensity  at  any  depth;  assuming  that  the 
planes  of  zero  pressure,  bounding  the  supporting  prism  of 
earth  to  have  a  slope  of  one-half  to  one. 

Weights  and  Dimensions  of  Electric  Cars. — The  weights 
assumed  for  the  electric  cars  in  the  preceding  classification 
may  seem  rather  large,  but  it  should  be  remembered  that 
the  stresses  in  the  bridge  depend  not  only  on  the  weight 
of  the  car,  but  also  on  the  wheel  base,  distance  between 
trucks,  etc.  The  dimensions  vary  with  the  locality  and  the 
weights  and  dimensions  chosen  are,  in  our  opinion,  justified. 

It  it  is  desired  to  make  a  special  design  the  following 
data  on  electric  cars  may  be  of  use.  The  values  given  must 
be  taken  as  approximate  averages.  The  weights  given  are 
for  the  loaded  car  and  include  the  weight  of  the  trucks. 

Small  cars,  such  as  are  used  in  small  towns,  four  wheels 
on  two  axles,  seating  twenty-eight  persons.  Car  body, 
20'0"x8'3";  over  all  length,  29'0";  distance  c.  to  c.  axles,  8'0"; 
weight,  11  tons. 

City  car  for  heavy  service,  seating  fifty-two  persons.  Car 
body,  34'0"x8'6";  over  all  length,  47'0";  wheel  base,  4'0"  to 
6'0";  c.  to  c.  trucks,  24'0";  weight,  15  tons. 

Large  interurban  cars,  seating  72  persons.  Car  body,  50'0"- 
x8'6";  over  all  length,  56'0";  wheel  base,  6'3";  c.  to  c.  trucks, 
30'0";  weight,  42  tons. 


DETAILED  DESIGN  OF  A  FLAT  SLAB  BRIDGE. 

The  following  example  illustrates  the  application  of  the 
methods  above  outlined: 

Problem. — Design  a  flat  slab  bridge,  resting  on  abut- 
ments, clear  span  16'0",  with  an  earth  fill  2'0"  deep.  Road- 
way to  be  16'0"  wide  in  the  clear,  Class  2  loading.  See 
Fig.  92-F. 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


217 


EAflTH  FIU, 


Fig.    92-F. 


In  the  design  we  will  consider  only  a  strip  of  bridge  12" 
wide  as  this  simplifies  matters.  The  section  will  be  made 
constant  across  the  width. 


DEAD  LOAD. 

Weight  of  fill  =  50  d(2s+d)  =  100(36)  =3,600  Ibs. 
Weight  of  slab  (assuming  thickness  =16")  = 

11A  X  150  X  16  =  3,200  Ibs. 

Total 6,800  Ibs. 

Bending  moment  =  1/&WI=  >^X6,800Xl6 

=  13,600  ft.  Ibs. 
Actual  dead-load  moment  =  163,200  inch  Ibs. 


LIVE  LOADS. 

For  this  span  maximum  stresses  will  be  caused  by  the 
concentrated  loads;  the  uniform  load  will  not  be  considered. 
We  will  determine  the  bending  moments  due  to  the  20-ton  roller 
and  to  the  40-ton  car,  using  the  larger  in  the  design. 

Road  Roller. — Maximum  moment  occurs  with  rear  wheels 
at  center  of  span.  Load  on  rear  wheels  equals  two-thirds 
of  40,000  pounds=26,700  pounds.  This  load  as  previously 
explained  (see  Fig.  92-D)  acts  on  a  line  7'6"  long;  the  distribu- 
tion on  the  slab  is  shown  by  the  following  diagram  (Fig.  92-G)  ; 


218 


REINFORCED    CONCRETE. 


the   broken   lines   indicate   the   area   of   slab   over   which   the 
load  is  distributed. 


•e'o"- 


Fig.    92-H. 

The  load   per  square   foot   on   area  2'0"    X    7'6"   =          ' 
=  1,780  Ibs. 

On  a  strip  of  bridge  12"  wide,  the  load  would  be  as  shown 
by  Fig.  92-H. 

Maximum  moment  at  center  of  span,  on   strip   12"  wide, 
=  ^/=(l,780x8)— (1,780X^)  =  13,400  ft.  Ibs. 
=161,000  inch  Ibs. 

Electric  Car. — The  maximum  moment  occurs  with  one 
truck  on  center  of  span.  Distribution  of  load  on  slab  is  as 
shown  by  diagram  (Fig.  92-1)  ;  assuming  ties  to  be  8  feet  long. 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


219 


\ 


'A 


*      s 

"I  « 


7-0 


\ 


The  full  line  shows 
area  over  which  truck 
load  is  distributed  by 
track  system;  the  brok- 
en lines  indicate  loaded 
area  of  slab. 

Load  per  square 
foot  of  loaded  area  = 
40,000-^90=445  Ibs. 


Fig.    92-1. 


The  load  on  a  strip  12"  wide  would  be  as  shown  by  the 
following  diagram,  Fig.  92-J. 


.9-0' 


/6~0' 


Fig.    92-J. 

Moment  at  center=yJ/=(2,OOOX8)— (2,OOOX2X)-=1 1,500  ft.  Ibs. 

=138,000  in.  Ibs. 

Adding  25%  for  impact,  moment^  172,000  in.  pounds. 

This  moment  is  larger  than  that  due  to  the  road  roller 
and  we  will  use  it  in  the  design. 


220  REINFORCED    CONCRETE. 

Using  a  factor  of  safety  of  two   on   the   dead   load   and 
four  on  the  live  load  we  have 

Ultimate  moment,  dead  load=2Xl61,000=    322,000  in.  Ibs. 
Ultimate  moment,  live  load=4X  172,000=    688,000  in.  Ibs. 


Designing  moment  =  /J/o  =  l,  010,000  in.  Ibs. 
We  can  determine  the  depth  of  slab  and  the  amount  of 
reinforcement   required   by   the   formula: 

71/0  =  370  fid*,  for  As  =  0.0085  bd. 


from  which  d=15" 

^8  =  0.0085X12X15  =  1.53  sq.  in. 

d=  distance  from  top  of  slab  to  the  center  of  the  rein- 
forcing bars,  we  will  add  \l/2"  of  concrete,  giving  1"  on  un- 
derside of  bars. 

Make  slab  16J4"  thick;  1"  corrugated  rounds  spaced  6" 
centers.  Bend  up  every  third  bar  at  the  sixth  point,  say  2'6" 
from  the  abutments. 

Transverse  Reinforcement.  —  To  properly  distribute  con- 
centrated loads  and  to  tie  the  bridge  in  the  transverse  direc- 
tion y2"  corrugated  rounds  will  be  placed  (over  the  main  re- 
inforcing bars)  crosswise  of  the  bridge,  and  12"  on  centers. 

Shearing  Investigation.  —  The  dead-load  shear  on  a  strip 
12"  wide  is  3,400  pounds. 

The  maximum  live-load  shear  occurs  when  the  rear  wheels 
of  the  road  roller  are  12"  inside  the  abutment,  and  is  equal  to 

3.S60X1S.  s 

16 
Total  shear  =  3,400+3,340  =  6,740  Ibs. 

At  the  allowed  stress  of  fifty  pounds  the  concrete  alone 
is  capable  of  carrying  12X15X50=9,000  pounds  of  vertical 
shear.  This  would  indicate  that  no  provision  for  shear  need 
be  made;  every  third  bar  will  be  bent  up,  however,  as  stated. 

Side  Walls  for  Retaining  Fill.—  It  will  not  be  necessary  to 
figure  these.  They  will  be  made  12"  thick  and  reinforced 
as  shown. 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


221 


Waterproofing.  —  Some  form  of  waterproofing  should  be 
used  and  the  top  surface  of  the  slab  arranged  for  drainage. 
The  top  surface  of  the  slab  will  be  as  shown  on  the  draw- 
ings. 

Bearing  on  Abutments.  —  All  concrete  bridges  resting  on 
abutments  shall  have  at  least  12"  bearing;  a  maximum  pres- 
sure of  fifty  pounds  per  square  inch  will  be  allowed  for  slab 
bridges. 


DETAILED  DESIGN  OF  A  GIRDER  BRIDGE. 

The  following  detailed  design  will  illustrate  the  applica- 
tion of  the  methods  advocated  to  the  design  of  a  girder 
bridge: 

Problem.  —  Design  a  girder  bridge,  resting  on  abutm'ents; 
clear  span  32'0";  earth  fill  15"  deep.  Bridge  to  be  24'0"  wide 
in  the  clear,  with  two  4'0"  sidewalks  and  car  track  on  center 
line.  Class  2  loading. 

The  cross-section  of  the  bridge  will  be  as  shown  on 
Fi-  92-K. 


#ir£#/rA7£  xcr/on 


Fig.    92-K. 


222  REINFORCED    CONCRETE. 

Floor  Slab. — The  minimum  thickness  of  floor  slabs  will 
be  taken  as  5".  This  thickness  of  slab  should  take  care  of 
extraordinary  concentrated  loads  such  as  might  be  caused 
should  a  car  be  derailed  on  the  bridge. 

To  provide  for  such  contingencies  all  slabs  for  girder 
bridges  will  be  designed  for  a  live  load  of  500  pounds  per 
square  foot,  in  addition  to  weight  of  slab  and  fill,  using  a 
factor  of  two  on  the  dead  and  four  on  the  live  load. 

Moments  will  be  figured  by  the  formula  M=  r2  zul2,  since 
the  slabs  are  continuous  over  three  or  more  supports;  /=dis- 
tance  c.  to  c.  of  beams. 

Design  of  Slab. — Dead  load  per  square  foot: 
.      Slab,  -&X150=  621bs. 
Fill,   jfXlOO=125  Ibs. 

Total,       18?  Ibs. 

Dead  load  moment=  A»/2=3SAXl87X25=«390  ft.  Ibs. 

Live  load  moment=  A X 500X25  =  1,040  ft.  Ibs. 

Designing  moment  =  ^0=  (2X1 2X  390)  +  (4  X  12  X  1,040)  = 
59,350  in.  Ibs. 

Taking  a  strip  of  slab  12"  wide,  we  can  find  the  thickness 
of  slab  and  the  amount  of  reinforcement  required  from  the 
formula  Mo  =  370  6d2,  in  which  ^s  =  0.0085  bd. 

Inserting  the  values  for  M0  and  b  in  this  formula,  we  find 
that  d=3.7  inches,  and  ^s  =  0.38  square  inches,  where  As  is  the 
section  of  reinforcing  steel  required  in  a  12-inch  width  of  slab. 

Since  we  have  made  the  thickness  of  the  slab  5",  d  will  be 
4",  which  is  greater  than  required  by  the  formula.  The 
amount  of  steel  required  may  accordingly  be  decreased,  and 
is  equal  to 

'     X0.38  sq.  in.  =  0.35  sq.  in. 

Slab  will  be  5"  thick,  reinforced  with  l/2"  corrugated  rounds 
placed  7"  on  centers. 

In  the  design  we  have  considered  the  slab  as  partially 
fixed  on  the  beams  and  to  provide  for  the  reverse  bending 
moment  developed,  reinforcing  bars  will  be  placed  in  the 
top  of  the  slab  over  the  beams;  the  amount  used  will  be 


BRIDGE  DESIGN  AND  CONSTRUCTION.  223 

one-half  that  required  in  the  bottom  of  the  slab  and  we  will 
use  l/2"  corrugated  rounds,  3'0"  long,  spaced  14"  on  centers. 
Note. — That  part  of   the   slab  under  the   sidewalks   will   be 
the  same  as  that  under  the  roadway. 

Girders. — In  all  girder  bridge  designs  the  length  center 
to  center  of  bearings  will  be  taken  equal  to  the  clear  span 
plus  one  foot.  This  length,  c.  to  c.  of  bearings,  will  be  used 
in  computing  the  stresses  developed.  It  is  desirable  to  have, 
brackets  at  the  ends  of  the  girders  when  conditions  permit, 
so  as  to  reduce  the  unit  vertical  shearing  stresses  and  gradu- 
ally unload  the  reaction  at  the  abutment  into  the  girder.  In 
all  girder  designs  special  provisions  for  taking  care  of  shear- 
ing and  diagonal  tensile  stresses  should  be  made.  Some  of 
the  main  reinforcing  bars  should  be  bent  up  near  the  ends 
of  the  girder  and  stirrups  used  throughout  the  length. 

Girder  Gl. — This  girder  will  be  figured  for  the  dead  load 
and  a  live  load  of  125  pounds  per  square  foot  on  the  walk. 
Dead  load  on  girder: 

Sidewalk,  AXl50X2#X32=  4,000  Ibs. 

Fill,  -HX100X2^X32=  7,350  Ibs. 

Slab,  AX150X2^X32  =  5,000  Ibs. 

Girder  (assumed  12"X36")  =  14,400  ibs. 

Total =30,750  Ibs. 

Dead  load  moment  =  >6  0Y=HX30,750X33  =  127,000  ft.  Ibs. 

Live  load,  125  Ibs.  per  square  foot. 

Live  load  on  girder  =  125X2^X33  =  10,000  Ibs. 

Live  load  moment  =*/&  #7=^X  10,000X33  =  41,200  ft.  Ibs. 

To  get  the  designing  moment,  use  a  factor  of  2  on  dead 
load  and  4  on  live  load,  minimum  to  be,  however,  3  (DL-f- 
LL.) 

^/0  =  3  (127,000+41,200)  X12  =  6,050,000  in.  Ibs. 

Applying  the  formula  Af0  =  37Q  dd2,  and  taking  b=\2",  we 
find  that  d=37";  ^s  =  0.0085  &/=3.76  square  inches. 

We  will  make  girder  12"  wide  and  40"  deep,  using  five 
1"  corrugated  rounds  and  bending  up  two  bars  as  shown,  at 
a  point  4'0"  from  each  abutment. 


224  REINFORCED    CONCRETE. 

Shearing  Provisions. — The  maximum  external  vertical 
shear  at  the  end  of  the  girder,  due  to  full  live  and  dead 
loads  equals  20,375  pounds. 

In  all  girder  designs  the  concrete  will  be  assumed  as 
capable  of  carrying  50  pounds  of  vertical  shear  over  the 
cross  section  bd.  Accordingly,  if  l/c=  total  shearing  value  of 
the  concrete,  we  have: 

Fc=12x37x50=22,2001bs. 

This  would  indicate  that  no  special  shearing  provisions 
are  necessary.  It  is  advisable,  however,  in  all  cases  to  make 
some  shearing  provisions,  and  we  will  use  U-shaped  stirrups 
of  l/2"  corrugated  rounds,  spaced  18"  throughout  the  length  of 
the  girder. 

Girder  G2. — This  will  be  designed  for  the  average  of  the 
stresses  in  girders  Gl  and  G3,  so  we  will  accordingly  figure 
girder  G3  first. 

Girder  G3. — Class  2  loading  requires  that  the  design  be 
based  on  the  maximum  stresses  produced  by  either  a  20- 
ton  road  roller  or  a  40-ton  electric  car/  (The  alternative 
live  load  of  125  pounds  per  square  foot  causes  much  smaller 
stresses  than  the  concentrated  loads.) 

The  two  girders  G3  will  be  designed  to  carry  the  total 
car  load. 

Each  girder  may,  however,  carry  two-thirds  of  the  road 
roller  concentrations;  the  full  load  on  the  front  wheel  and 
one-half  of  the  load  on  the  two  rear  wheels. 

All  interior  girders  on  single  span  bridges  should  be  fig- 
ured as  T-beams. 

.Dead  load  on  girder: 

Fill,    HxlOOX5x32  =  20,0001bs. 
Slab,  AX150X5X32  =  10,000  Ibs. 

Girder  (assume  450  Ibs.  per  ft.)  =  14,400  Ibs. 

Total =44,400  Ibs. 

Dead  load  bending  moment: 

J/=}fJF/=^X44,400x33  =  183,000  ft.  Ibs. 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


Live  Loads.  —  Maximum  moment  due  to  road  roller. 


225 


We  will  assume  that  only  one  road  roller  will  be  on  the 
bridge  at  any  one  time.  The  maximum  load  on  one  girder 
then  may  be  represented  by  two  concentrated  loads  of  13,300 
pounds  each,  11  '0"  on  centers.  The  maximum  moment  will 
occur  with  one  of  the  loads  2'9"  off  center  of  span,  as  shown 
Fig.  92-L. 


Fig.    92-L. 


Since  the  fill  is  but  15"  deep,  the  effect  of  the  fill  in  distri- 
buting the  loads  will  be  neglected  in  determining  the  mo- 
ment on  the  girder. 


13,300X8.25^13,300X19.25 


=  11,100  Ibs. 


33  33 

M=  13.75X11,100=  153,000  ft.  Ibs. 

Maximum  moment  due  to  electric  car. 

For  assumed  distribution  of  load  by  track  system,  see 
Fig.  92-E,  p.  215. 

The  maximum  moment  will  occur  with  one  truck  at  the 
middle  of  the  span,  the  other  truck  being  off  the  bridge. 
(Two  cars  following  each  other  will,  for  this  span,  produce 
practically  the  same  moment  as  one  car.  See  sketch  of 
standard  forty-ton  car,  Fig.  92-A.) 


226  REINFORCED    CONCRETE. 


Fig.    92-M. 

The    loading    for    maximum    moment    will    be    as    shown 
by  Fig.  92-M  ;  where  the  load  given  is  that  on  one  girder. 

#=(10,OOOX16K)—  (10,000X1.75)  =147,500  ft.  Ibs. 

To   this   static  moment  add  25%   for  impact  for   rapidly 
moving  loads,    giving  a  moment  of  184,000  foot-pounds. 

The  maximum  moment  then  due  to  the  specified  live  loads 
is  184,000  foot  pounds. 

Designing  moment: 

M0=(  (2X183,000)+(4X  184,000)  \  12  =  13,224,000  in.  Ibs. 

For  the  design  of  T-beams  we  will  use  the  formula 


M0=O.S6  Fp  ^2  =  43,000^  dd2,  using  high  elastic  limit  cor- 
rugated bars. 

Assume  d—Z2"  and  £=14",  we  then  have 

M0  =  13,224,  000=  43,  OOOX14X322X/> 
from  which  />  =  .0215 

AS  =  .  0215X14X32  =  9.65  square  inches. 

We  will  make  the  girder  36"  deep  over  all  and  use  eight 
1/4"  corrugated  rounds. 

For  this  length  of  beam  there  is  no  danger  of  failure  by 
horizontal  shear  along  the  horizontal  or  vertical  planes  of 
attachment  of  the  stem  to  the  flange.  The  distance  between 
beams  is  S'O",  and  the  amount  of  reinforcement  used  =  0.0215 
bd,  where  b  =  14";  corresponding  to  an  average  percentage 
of  reinforcement  for  the  full  width  of  slab  of  one-half  of  1 


BRIDGE  DESIGN  AND  CONSTRUCTION.  227 

per  cent.  This  indicates  that  there  is  ample  width  of  slab  be- 
tween beams  for  T-beam  action. 

Shearing  Provisions. — The  vertical  external  shear  at  the 
end  of  the  beam,  due  to  dead  load  is  22,200  pounds,  the  load 
per  foot  of  girder  being  1,380  pounds. 

The  shear  at  the  end  of  the  girder  due  to  the  car  would 
be  practically  a  maximum  when  the  center  of  one  truck  is 
3'6"  from  the  abutment;  this  total  vertical  shear  may  be 
taken  equal  to  20,000  pounds. 

The  total  maximum  shear  at  end  of  girder  =  42,200pounds. 

In  providing  for  vertical  shear  we  will  assume  that  the 
concrete  carries  fifty  pounds  per  square  inch  on  the  section 
dd,  and  put  in  steel  to  carry  the  excess. 

Steel  for  reinforcing  against  diagonal  tensile  and  shear- 
ing stresses  will  consist  of  bent  up  main  reinforcing  bars  and 
loose  stirrups. 

In  the  design  we  will  neglect  the  effect  of  the  bent  up  bars. 

(If  bent  up  bars  are  figured  to  carry  the  diagonal  compon- 
ent of  the  vertical  shear  in  the  "panel"  in  which  they  occur, 
limit  the  direct  tensile  stress  to  12,000  Ibs.  per  sq.  inch.) 

Loose  vertical  stirrups  will  be  figured  by  the  formula 

0.86  dP_  0.86  dP 
y~  V—  Fc  ~  V—  SOXfid 

Where  y=spacing  of  stirrups  required  at  any  section, 

F=total  stress  in  one  stirrup=total  cross  section- 
al area  of  the  vertical  legs  of  the  stirrup  times 
the  allowed  unit  stress    (16,000  Ibs.). 
F=external  vertical  shear  at  any  section. 
Fc=total  vertical  shearing  stress  that  the  concrete 
is  assumed  to  be  capable  of  taking=Fc  X  bd. 

If  the  stirrups  are  to  be  figured  to  carry  all  the  vertical 
shear  without  assistance  from  the  concrete,  use  the  formula 


228 


REINFORCED    CONCRETE. 


Should  it  be  desired  to  include  that  part  of  the  vertical 
shear  assumed  to  be  carried  by  the  bent  up  bars  the  for- 
mula becomes 


0.86  dP 


whlch 


y&  =  amount  of  vertical  shearing  stress  carried  by 
bent  up  bars. 

The  following  table  gives  the  data  necessary  to  deter- 
mine the  required  stirrup  spacing,  neglecting  the  effect  of 
the  bent  up  bars: 

Stirrups—  U-shaped,   y2"   Corrugated   Rounds,   P=6,080. 


TABLE  LIX-B. 


Distance  from 
Abutment. 

Vert.  Ext. 
Shear, 
V. 

Vc 

V—  Vc 

Required 
Spacing, 

y. 

0 

42,200 

22,400 

19,800 

8.4' 

2 

38,400 

22,400 

16,000 

10.4' 

4 

33,200 

22,400 

10,800 

15.5' 

6 

28,400 

22,400 

6,000 

27.9' 

8 

24,200 

22,400 

1,800 

12 

16,100 

22,400 

We  will  make  spacing  nine  inches  for  a  distance  of  six 
feet  from  the  abutment,  increasing  the  spacing  to  eighteen 
inches  beyond  this  point. 

Bent-Up  Bars — Bend  up  two  reinforcing  bars  at  a  point 
6'6*  from  abutment,  and  two  additional  bars  3'3"  from  abut- 
ment. 

Girder  G2 — In  designing  this  girder  we  will  take  the 
average  of  the  moments  in  girders  Gl  and  G3. 


J!fothen=   */2    (6,050,000+13,224,000)^9,637,000    in.    Ibs. 


BRIDGE  DESIGN  AND  CONSTRUCTION.  229 

This  girder  will  be  made  the  same  size  as  G3;  the 
amount  of  reinforcing  steel  required  may  be  determined 
by  the  formula 


9,637,000=50,000  ^8X0.86X32 
from    which  As  =7.0    square    inches. 

Make  girder  36"xl4"  as  before,  using  seven  \l/%"  corru- 
gated rounds.  Bend  up  one  bar  6'6"  from  end  and  two  bars 
3'3"  from  abutment.  Stirrups:  use  l/2"  corrugated  rounds 
same  spacing  as  in  G3. 

Bearing  of  Bridge  on  Abutment  —  In  order  to  properly 
distribute  the  load  and  provide  for  sufficient  bearing  area 
the  bridge  will  be  made  solid  for  the  full  depth  of  the  gird- 
ers, where  it  rests  on  the  abutment.  This  construction  is 
desirable  on  all  girder  bridges,  owing  to  the  rigidity  and 
general  stiffness  given  by  the  solid  end. 


-4 


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BRIDGE  DESIGN  AND  CONSTRUCTION. 


233 


TABLE  LIX-C. 
STANDARD  DESIGNS— FLAT  SLAB  BRIDGES. 

LIGHT  HIGHWAY  SPECIFICATION. 
Class  No.  1  Loading.     12-ton  Road  Roller. 


d=  depth    of 
fill. 
t=thickness 
of  con- 
crete. 
f=bearing 
on  abut- 
ment. 

Main  Reinforcement 
Corr.  Rounds. 
Every  third  bar  bent 
up  as  shown. 

Bars  A. 

llff 

i  is  i 

Illlf 

•S  fc;  gj> 

*~   Np<            .t«  "23      .f. 

_2,-\   .  3-3  £ 

Hill 

11 

d. 

t. 

f. 

Size. 

Spa. 

No. 

L'gth. 

Number 
Required. 

Number 
Required. 

No. 

Length. 

No. 

Length. 

CLEAR  SPAN,  6'-0*. 

2' 
4' 

6' 
8' 

8" 
8" 
9" 
10" 

12" 
12" 
12" 
12" 

W- 

35 

38 
38 
30 

7'-6" 
7'-6" 
7'-6" 

9 
9 
9 
9 

None. 
9 
9 
9 

18 
18 
'18 

18 

2'-9" 
4'-9* 
6'-9* 
8'-9" 

10 
14 
20 
26 

7'-6" 
7'-6" 
7'-6" 
7'-6* 

CLEAR  SPAN,  8'-0*. 

2' 

4' 
6' 
8' 

10" 
10" 
11" 
12" 

12" 
12" 
12" 
12" 

1 

7     " 
6     ' 

5     * 

30 
35 
38 
42 

9'-6" 
9'-6" 
9'-6" 
9'-6" 

11 
11 
11 
11 

None. 
11 
11 
11 

22 
22 
22 
22 

2'-9" 
4'-9* 
7'-0* 
9'-0" 

10 
14 
20 

26 

9'-6" 
9'-6" 
9'-6" 
9'-6* 

CLEAR  SPAN,  lO'-O*. 

2' 
4' 

6' 
8' 

11"|  12" 
12"   12" 
13"   12" 

15"|  12" 

w* 

35 
38 
32 
35 

iii 

13 
13 
13 
13 

None. 
13 
13 
13 

26 
26 
26 
26 

3'-0" 
5'-0* 
7'-0* 
9'-3" 

10 
14 
20 
26 

j| 

CLEAR  SPAN,  12'-0". 

2' 
4' 
6' 
8' 

12" 
14" 
15" 
17" 

12" 
12" 
12" 
12" 

S|| 

38 
32 
38 
32 

13'-6]| 

15 
15 
15 
15 

None. 
15 
15 
15 

30 
30 
30 
30 

3'-0" 
5'-3" 
7'-3* 
9'-6" 

10 
14 
20 
26 

13'1" 

CLEAR  SPAN,  14'-0". 

2' 
4' 
6' 

8' 

14'i  12" 

151  12" 
17"i  15* 
19"   15" 

\<> 

6H'|  32 

6  2"  35 
5^1  38 

K 

17 
17 
17 
17 

None. 
17 
17 
17 

34 
34 
34 
34 

3'-3* 
5'-3" 
7'-6" 
9'-6" 

10 
14 
20 
26 

16'-0* 

CLEAR  SPAN,  16 -0. 


V 

15" 

12* 

7^* 

5V4" 

38 

17'-6" 

19 

None. 

38 

3'-3" 

10 

17'-6* 

4' 

17" 

12" 

6  * 

35 

17'-6" 

19 

19 

38 

5'-6* 

14 

17'-6* 

r/ 

19" 

15" 

1  ' 

W" 

38 

18'-0" 

19 

19 

38 

7'-6* 

20 

18'-0* 

8' 

21" 

15" 

1  " 

4X2" 

46 

18'-0" 

19 

19 

38 

9'-9" 

26 

18'-0" 

CLEAR  SPAN,  18'-0". 


V 

16" 

15" 

ys"\5     "\  42 

20'-0" 

21 

None. 

42 

3'-3* 

10 

20'-0" 

4' 

19" 

15" 

1     "5^*1  38 

20'-0" 

21 

21 

42 

5'-6" 

14 

20'-0" 

V 

21" 

18" 

1     J4HJ  46 

20'-6" 

22 

22 

44 

7'-9" 

20 

20'-6" 

8' 

23" 

20" 

I^ISH'I  38 

20'-9" 

22 

22 

44 

lO'-O" 

26 

20'-9" 

CLEAR  SPAN,  20'-0". 


2' 

18" 

15" 

1     "16     '1  35  |22'-0" 

23 

None. 

46 

3'-6" 

10 

22'-0" 

4' 

21" 

15" 

1     ",5     "|  42  22'-0" 

23 

23 

4fi 

5'-9" 

14 

22'-0" 

6' 

23" 

18" 

l^'SM"!  38  22'-6" 

24 

24 

48 

8'-0" 

20 

22'-6" 

8' 

26"|  20" 

1H'5     "1  42  |22'-9" 

24 

24 

48 

10'-3" 

26 

22'-9* 

234 


REINFORCED    CONCRETE. 


TABLE  LIX-D. 

STANDARD  DESIGNS— FLAT  SLAB  BRIDGES. 
HEAVY  HIGHWAY  SPECIFICATION. 

Loading.    20-ton  Roller  or  40-ton  Car. 


d  =  depth     of 

fill. 

t=thickness 
of  con- 
crete. 

f  =  bearing 
on  abut- 
ment. 


Main  Reinforcement 
Corr.  Rounds. 

Every  third  bar  bent 
up  as  shown. 

Bars  A. 


I*  •!!' 

•s-sslt 

WSo!z:£ 


d. 


t.      f.    Size.  Spa 


No.  L'gth 


Number        Number 
Required.      Required. 


No 


Length. 


No. 


Length. 


CLEAR  SPAN,  6'-0*. 


2' 
4' 
(i' 
8' 

OOCOCC 

to  to  to  to 

^"5     *  42 
%*<5     "l  42 
%"\71A"\  28 
34*|6     "|  35 

7M5" 

7'-6" 
7'-6" 

9 
9 
9 
9 

None. 
9 
9 
9 

18 
18 
18 
18 

2'-9" 
4'-9" 
6'-9* 
8'-9" 

10 
14 
20 

26 

7'-6" 
7'-6" 
7'-6" 

7'-G" 

CLEAR  SPAN,  8'-0". 


2' 
4' 
6' 
8' 

11" 
11" 
12" 
13" 

12" 
12" 
12" 
12" 

W- 

38 
38 
38 
30 

2222 

11 
11 
11 
11 

None. 
11 
11 
11 

22 
22 
22 
22 

3'-0" 
5'-0* 
7'-0" 
9'-0* 

10 
14 

20 
26 

9'-6" 
9'-6" 
9'-6* 
9'-6" 

CLEAR  SPAN,  lO'-O*. 

2' 
4' 
6' 

8' 

12" 
13* 
14" 
15" 

12" 
12" 
12" 
12" 

H' 

5  ' 

s  2" 

42 
32 
35 
38 

!!$ 

13 
13 
13 
13 

None. 
13 
13 
13 

26 
26 
26 
26 

3'-0" 
5'-0" 
7'-3* 
9'-3" 

10' 
14 
20 
26 

11:? 

CLEAR  SPAN,  12'-0*. 


2' 
4' 
(i' 
8' 

14" 
15" 
16" 
17" 

12" 
12" 
12* 
12* 

7*' 

6" 
6" 
5* 
6" 

35 
35 
42 
35 

CO  CO  CO  CO 
O2  O2  O2  O5 

15 
15 
15 
15 

None. 
15 
15 
15 

30 
30 
30 
30 

3'-3" 
5'-3" 
7'-3" 
9'-6" 

10 
14 
20 
26 

|| 

CLEAR  SPA 

N,  14'-0". 

2' 

4' 
(i' 
8' 

17" 
18" 
20" 

12" 
12* 
15" 
15" 

K" 

5     * 
5     " 

42 
38 
38 
42 

15'-6" 
15'-6" 
16'-0" 
16'-0* 

17 
17 
17 
17 

None. 
17 
17 
17 

34 
34 
34 
34 

3'-3" 
5'-6" 
7'-6* 
9'-9" 

10 
14 
20 
26 

15^-6" 

CLEAR  SPAN,  16'-0". 

2' 
4' 
6' 

8' 

18" 
18" 
20" 

22" 

12" 
12" 
15" 
15" 

H" 

6     " 

5  2" 
6     " 

35 
38 
42 
35 

ll'Io' 

19 
19 
19 
19 

None. 
19 
19 
19 

38 
38 
38 
38 

3'-6" 
5'-6" 
7'-9" 
9'-9" 

10 
14 
20 
26 

F<T 

CLEAR  SPAN,  18'-0". 


2' 

19" 

15" 

5U" 

,SS 

20'-0" 

21 

None. 

42 

3'-6" 

10 

20'-0" 

4' 

21* 

15" 

1  " 

4V4" 

40 

20'-0" 

21 

21 

42 

5'-9" 

14 

20'-0" 

()' 

22" 

18" 

IVT 

6  " 

35 

20'-6" 

22 

22 

44 

7'-9" 

20 

20'-6" 

S' 

24* 

20"| 

IK" 

5  " 

42 

20'-9" 

22 

22 

44 

lO'-O" 

26 

20'-9* 

CLEAR  SPAN,  20'-0". 


2' 

21" 

15" 

1     * 

5     " 

42 

22'-0" 

23 

None. 

46 

3  '-9" 

10 

22'-0" 

4' 

22" 

15" 

m* 

6     " 

35 

22'-0" 

23 

23 

46 

5'-9" 

14 

22'  -0" 

6' 

24" 

18" 

\w 

5     " 

42 

22'-6" 

24 

24 

48 

8'-0" 

20 

22'-6" 

8 

27" 

20* 

iys" 

4H" 

46 

22'-9" 

24 

24 

48 

10'-3" 

26 

22'-9" 

BRIDGE  DESIGN  AND  CONSTRUCTION. 


235 


TABLE  LIX-E. 
STANDARD  DESIGNS— FLAT  SLAB  BRIDGES. 

CITY  HIGHWAY  SPECIFICATION. 
Class  No.  3.    Loading.    20-ton  Roller  or  60-ton  Car. 


d  —  depth    of 
fill, 
t  —  thickness 
of  con- 
crete, 
f  —  bearing 
on  abut- 
ment. 

Main  Reinforcement 
Corr.  Rounds. 
Every  third  bar  bent 
up  as  shown. 

Bars  A. 

AUfl 

rig* 

If^s 

>  rt       *    pQ 

1st? 
i.sc3s 

Tranverse  Rein- 
forcement in  top 
of  slab.  H"Corr. 
Rounds.  17  '0' 
Long. 
Bars  C. 

sga.2 

aP^-S   .0 

—  SN     .fc.2  a, 

•3   jil  5 

SrflfS*" 

Illil   : 

Horizontals  in 
Side  Walls.  H* 
Corr.  Rounds. 
Number  required 
for  both  walla. 
Bars  E. 

d. 

t. 

f. 

Size. 

Spa. 

No. 

L'gth. 

Number 
Required. 

Number 
Required. 

No. 

Length. 

No. 

Length. 

CLEAR  SPAN  6'-0'. 


2' 

11' 

12' 

34' 

&/<>' 

32 

7'-6' 

9 

None. 

18 

3'-0' 

10 

7'-6' 

4' 

11' 

12" 

Z4' 

VM* 

32 

7'-6" 

9 

9 

18 

5'-0' 

14 

7'-6' 

6' 

11' 

12" 

*/*' 

W/o" 

32 

7'-fi' 

9 

9 

18 

7'-0' 

20 

7'-6' 

8' 

11' 

12" 

%" 

6     ' 

35 

7  '-6' 

9 

9 

18 

9'-0' 

26 

7  '-6' 

CLEAR  SPAN, 


2' 
4' 
6' 

8' 

12'j  12' 
12'  12' 
12"  12' 
13"|  12' 

K 

£ 

5  ' 
5  ' 

6H* 

42 
42 
42 
32 

9'-6' 
9  '-6' 
9'-6' 
9'-6' 

11 
11 
11 
11 

None. 
11 
11 
11 

22 
22 

22 
22 

3'-0' 
5'-0' 
7'-0' 
9'-0' 

10 
14 

20 
26 

SP-6* 
9'-6' 
9'-6' 
9'-6' 

CLEAR  SPAN,  lO'-O". 


2' 

14" 

121 

V*" 

w 

32 

ir-6' 

13 

None. 

26 

3  '-3" 

10 

11  '-6' 

4' 

14" 

12" 

W 

VM' 

32 

ll'-6" 

13 

13 

26 

5'-3" 

14 

ir-6* 

6' 

14" 

12" 

%' 

6     ' 

35 

ll'-6" 

13 

13 

26 

7'-3" 

20 

ll'-6' 

8' 

15" 

121 

y8" 

5W 

38 

ll'-6" 

13 

13 

26 

9  '-3" 

26 

ll'-6' 

CLEAR  SPAN,  12'-0'. 


2' 

16" 

12* 

t/«' 

5' 

42 

13-6' 

15 

None. 

30 

3  '-3" 

10 

13  '-6' 

4' 

16" 

12" 

«' 

5' 

42 

13'-6' 

15 

15 

30 

5'-3" 

14 

13'-6* 

6' 

16" 

12' 

%' 

5' 

42 

13  '-6' 

15 

15 

30 

7  '-3" 

20 

13'-6' 

S' 

17' 

12" 

1  " 

6' 

35 

13  '-6" 

15 

15 

30 

9'-6" 

26 

13'-6' 

CLEAR  SPAN,  14'-0' 


2' 

19" 

12" 

1" 

5V*" 

38 

15'-6" 

17 

None. 

34 

3  '-6* 

10 

15'-6' 

4' 

19" 

12' 

1' 

WA1 

38 

15  '-6' 

17 

17 

34 

5  '-6' 

14 

15'-6* 

6' 

19" 

15" 

r 

VA' 

38 

16'-0' 

17 

17 

34 

7'-6' 

20 

16'-0' 

8' 

20" 

151 

i" 

5  " 

42 

16'-0" 

17 

17 

34 

9'-9' 

26 

16'-0' 

CLEAR  SPAN,  16'-0*. 


•>' 

21' 

12" 

1  " 

5" 

42 

17'-6" 

19 

None. 

38 

3  '-9" 

10 

17'-6' 

4' 

21" 

12" 

1  " 

5* 

42 

17'-6" 

19 

19 

38 

5'-9" 

14 

17'-6' 

6' 

21" 

15" 

1  " 

5* 

42 

18'-0" 

19 

19 

38 

7'-9" 

20 

18'-0" 

8' 

22' 

15" 

\%" 

6" 

35 

18'-0" 

19 

19 

38 

9'-9* 

26 

18'-0* 

CLEAR  SPAN,  18'-0". 


2' 

22" 

15" 

m" 

6* 

35 

20'-0" 

21 

None. 

42 

3  '-9" 

10 

20'-0' 

4' 

22' 

15" 

m' 

6" 

35 

20'-0" 

21 

21 

42 

5'-9* 

14 

20'-0' 

6' 

22" 

18" 

mr 

6' 

35 

20'-6" 

22 

22 

44 

7  '-9' 

20 

20'-6' 

8' 

24" 

20" 

\w 

"5" 

42 

20'-9" 

22 

22 

44 

lO'-O" 

26 

20'-9' 

CLEAR  SPAN,  20'-0'. 


2' 

24" 

15" 

11/" 

WA' 

38 

22  '-0" 

23 

None. 

46 

4'-0" 

10 

22'-0' 

4' 

24" 

T5" 

m" 

WA* 

38 

22  '-0" 

23 

23 

46 

6'-0' 

14 

22'-0' 

6' 

24" 

18" 

m" 

5  " 

42 

22  '-6" 

24 

24 

48 

8'-0' 

20 

22'-6" 

S' 

27" 

20" 

w 

4J/2" 

46 

22  '-9" 

24 

24 

48 

10'-3" 

26 

22"9* 

236  REINFORCED    CONCRETE. 

COMPLETE  DESIGNS  OF  GIRDER  BRIDGES  FOR 
SPANS  FROM  TWENTY  TO   FORTY   FEET. 

Reference  drawings:  Figs.  92-Q,  92-R  and  92-S.  (See  also 
Detail  Sheets  for  Girders  Gl,  G2  and  G3.) 

Reinforcing  Steel. — Mechanical  bond  bars,  elastic  limit, 
50,000  Ibs. 

The  following  tables,  in  conjunction  with  Figs.  92-Q,  R 
and  S,  and  the  three  sheets  of  details,  showing  slab 
and  girder  construction,  give  the  complete  design  of  Girder 
Bridges  for  spans  of  twenty,  twenty-five,  thirty,  thirty-five 
and  forty  feet. 

The  standard  bridges  have  been  figured  for  the  three 
classes  of  loadings,  but  with  only  one  depth  of  fill — eighteen 
inches.  A  minimum  depth  of  fill  of  twelve  inches  is  re- 
quired on  all  girder  bridges.  The  slab  has  in  all  cases  been 
made  five  inches  thick. 

The  two  girders  under  the  car  tracks  have  been  figured  to 
carry  the  full  car  load.  Girders  Gl  in  Class  1  and  Class  2 
Bridges,  and  Girders  G2  in  Class  3  Bridges  have  been  de- 
signed for  that  proportion  of  the  roller  load  which  may 
come  upon  them.  For  the  sake  of  uniformity  Girders  G2  in 
Class  3  Bridge-s  have  been  made  the  same  depth  as  Girders 
G3. 

The  standard  designs  for  Class  3  Bridges  are  based  on  the 
sections  shown  in  Fig.  92-S,  page  241.  The  tables,  however, 
apply  just  as  well  to  the  "Alternate  Section,"  which  may  be 
preferred  by  some  engineers. 


238 


REINFORCED    CONCRETE. 


TABLE  LIX-F. 
CLASS  1— BRIDGES. 

GIRDERS  Gl. 
See  Detail  Sheet,  Page  243. 


Clear 
Span. 

h. 

b. 

f. 

Reinforcement. 

Bent  Bars. 

Stirrups. 

20'-0" 

32" 

12" 

15" 

6-%"  Corr.  Rounds. 

In  Beams  with  6  Bars 
Bend  up  1  Bar  at  the  $  Point. 
Bend  up  2  Bars  at  the  ^  Point. 

In  Beams  with  8  Bars 
Bend  up  2  Bars  at  the  \  Point. 
Bend  up  2  Bars  at  the  ^  Point. 

l/z  *  Corr.  Rounds  Bent  as  Shown  on 
Detail  Drawing. 

Spacing:  12'  to  the  i  Point, 
18  "Beyond. 

25  '-0" 

38" 

12" 

15" 

6-7A'-'  Corr.  Rounds. 

30'-0" 

44" 

12" 

15" 

3-7/s"   Corr.  Rounds. 
3-1"     Corr.  Rounds. 

35  '-0" 

50" 

14* 

18" 

6-1"     Corr.  Rounds. 

40'-0" 

53" 

15" 

21" 

8-1  *     Corr.  Rounds. 

GIRDERS  G2. 
See  Detail  Sheet,  Page  244. 


20'-0" 

25" 

12" 

15" 

6-1  "     Corr.  Rounds. 

§ 

.  'a        -"  "3 

a 

25'-0" 

29" 

14" 

15" 

8-1  "     Corr.  Rounds. 

•gP-i           ^RP-i 

1         ^ 
2          a 

.al         II 

a      -3 

30'-0' 

34" 

14" 

15" 

8-1  J/s"  Corr.  Rounds. 

§     .        ~«-o 

«  «  2   «  £2 

co  b  fe      oo  b  ' 

^•-    1  1 

jap^n     ^apppQ 

3  1    -Sn 

35  '-0" 

39" 

14" 

18" 

4-1^  "Corr.  Rounds. 
4-1  \i"  Corr.  Rounds. 

•g  rH  IM        -g  <M  (M 

O*  D«             Q.  O< 
|  3  3         §  3   3 

1  ? 

40'-0" 

47" 

14" 

21" 

8-1M*  Corr.  Rounds. 

-w  -a* 

-"   * 

SLAB. 

5*  Thick;  J^"  Corr  Rounds,  6"  Cts.  in  Bottom  of  S-ab. 
Top  Bar,   YI"  Corr.  Rounds  3'-0 '  long,  12"  Cts.  over  G2. 
Top  Bars,  H"  Corr.  Rounds  2MT  long,  12"  Cts.  at  Gl. 
1-Yi  *  Corr.  Rounds  lengthwise  of  Bridge  in  Each  Panel. 


240 


REINFORCED    CONCRETE. 


TABLE  LIX-G. 
CLASS  2— BRIDGES. 

GIRDERS  Gl. 
See  Detail  Sheet.  Page  243. 


Clear 
Span. 

h. 

b. 

f. 

Reinforcement. 

Bent  Bars. 

Stirrups. 

20  '-0' 

36' 

12' 

15' 

3-%  '  Corr.  Rounds. 
3-1  'Corr.  Rounds. 

In  Beams  with  6  Bars 
Bend  up  1  Bar  at  the  j  Point. 
Bend  up  2  Bars  at  the  ^  Point. 

In  Beams  with  8  Bars 
Bend  up  2  Bars  at  the  J  Point. 
Bend  up  2  Bars  at  the  &  Point 

3/2  '  Corr.  Rounds  Bent  as  Shown 
Detail  Drawing. 

Spacing:  12  'to  the  i  Point, 
18  'Beyond. 

25'-0' 

43" 

12' 

15' 

3-^'  Corr.  Rounds. 
3-1  '  Corr.  Rounds. 

30'-0' 

47' 

14" 

15' 

3-1  '     Corr.  Rounds. 
3-1K'  Corr.  Rounds. 

35  '-0' 

52' 

14" 

18" 

6-1K"  Corr.  Rounds. 

40'-0" 

58' 

16" 

21' 

4-1   '  Corr.  Rounds. 
4-1H"  Corr.  Rounds. 

GIRDERS  G2. 
See  Detail  Sheet,  Page  244. 


20'-0" 

31" 

14' 

15" 

8-1  '    Corr.  Rounds. 

In  Beams  with  8  Bars 
Bend  up  1  Bar  at  the  $  Point. 
Bend  up  2  Bars  at  the  &  Point. 

In  Beams  with  10  Bars 
Bend  up  2  Bars  at  the  J  Point. 
Bend  up  3  Bars  at  the  ^  Point. 

Yz"  Corr.  Rounds  Bent  as  Shown  on 
Detail  Drawing. 

Spacing:  9  '  to  the  1  Point, 
18*  Beyond. 

25  '-0" 

34" 

14* 

15" 

8-1M*  Corr.  Rounds. 

30'-0* 

39" 

14* 

15" 

4-1H"  Corr.  Rounds. 
4-1J4*  Corr.  Rounds. 

35  '-0" 

43' 

14' 

18' 

8-1M*  Corr.  Rounds. 

40'-0* 

47' 

17" 

21" 

10-1  Ji"  Corr.  Rounds. 

SLAB. 

5*  Thick,  Yz"  Corr.  Rounds,  6"  Cts.  in  Bottom  of  Slab. 
Top  Bars,  Yz*  Corr.  Rounds  3'-0 '  long,  12'  Cts.  over  G2. 
Top  Bars,  Yi*  Corr.  Rounds  2'-0"  long,  12"  Cts.  at  Gl. 
"2-Yz*  Corr.  Rounds  lengthwise  of  Bridge  in  Each  Panel. 


242 


REINFORCED    CONCRETE. 


TABLE  LIX-H. 

CLASS  3— BRIDGES. 

GIRDERS  Gl.    See  Detail  Sheet,  Page  243. 


Clear 
Span. 

h. 

.  b. 

f. 

Reinforcement. 

Bent  Bars. 

Stirrups. 

20'-0' 

30* 

12" 

15" 

6-%"  Corr.  Rounds. 

In  Beams  with  6  Bars 
Bend  up  1  Bar  at  the  $  Point. 
Bend  up  2  Bars  at  the  &  Point. 

In  Beams  with  8  Bars 
Bend  up  2  Bars  at  the  I  Point. 
Bend  up  2  Bars  at  the  ^  Point. 

y<i*  Corr.  Rounds  Bent  as  Shown  on 
Detail  Drawing. 

Spacing:  12*  to  the  i  Point, 
18"  Beyond. 

25  '-0* 

38" 

12" 

15" 

6-Ji*  Corr.  Rounds. 

30'-0" 

45" 

12" 

15" 

3-%*   Corr.  Rounds. 
3-1  "     Corr.  Rounds. 

35  '-0* 

50* 

14" 

18" 

6-1  "     Corr.  Rounds. 

40  '-0* 

56* 

15" 

21" 

8-1  *     Corr.  Rounds. 

GIRDERS  G2.    See  Detail  Sheet,  Page  244. 


20'-0* 

34" 

12* 

15* 

6-1  *     Corr.  Rounds. 

In  Beams  with  6  Bars 
Bend  up  1  Bar  at  the  I  Point. 
Bend  up  2  Bars  at  the  ^  Point. 

In  Beams  with  8  Bars 
Bend  up  2  Bars  at  the  I  Point. 
Bend  up  2  Bars  at  the  T\,  Point. 

y<i  "  Corr.  Rounds  Bent  as  Shown  on 
Detail  Drawing. 

|| 
co 

25'-0* 

39" 

14* 

15* 

8-1  *     Corr.  Rounds. 

30'-0' 

44* 

14" 

15* 

4-1  "     Corr.  Rounds. 
4-1^  "  Corr.  Rounds. 

35  '-0* 

47* 

14" 

18" 

4-lJ^  *  Corr.  Rounds. 
4-lK  "  Corr.  Rounds. 

40'-0" 

54" 

14* 

21" 

8-1  y±'  Corr.  Rounds. 

GIRDERS  G3.    See  Detail  Sheet,  Page  245. 


20'-0* 

34" 

14" 

15* 

8-  \Y8"  Corr.  Rounds. 

-^"S             *5"fl 

§ 

a 

E 

25'-0* 

39* 

14" 

15" 

4-1  Y%  "Corr.  Rounds. 
4-1^  "Corr.  Rounds. 

!^  £1 

1          «- 

r/.                  C) 

30'-0* 

44* 

14" 

15" 

8-1  Ji*  Corr.  Rounds. 

^  jq        aj^J 

2^"^      2^-^ 
^"S"S     pqlals 

Sl|    21§ 

a         ^   ' 

«    M       "aT  0 

i*  11 

35'-0* 

47" 

17* 

18" 

10-1M"  Corr.  Rounds. 

.gqqpq     .aeqcq 
•"g  <M  e^i     -r  <N  co 

!§•§•    i^S- 
g-g-s    §-g^ 

ij  Ca 

o|       g5 

40'-0" 

54" 

17* 

21" 

10-1M"  Corr.  Rounds. 

«^^    «^cS 

i    1 

SLAB 

5*  Thick,  Yi"  Corr.  Rounds,  6"  Cts.  in  Bottom  of  Slab. 
Top  Bars,  Y-i"  Corr.  Rounds  3'-0"  long,  12"  Cts.  over  G2  and  G3. 
Top  Bars,  yz"  Corr.  Rounds  2'-0"  long,  12"  Cts.  at  Gl. 
2H*  Corr.  Rounds  lengthwise  of  Bridge  in  Each  Panel. 


246  REINFORCED    CONCRETE. 

ARCH  BRIDGES. 
CURRENT  METHODS. 

Classification  of  Arch  Bridges. — Arch  bridges  are  far  more 
numerous  than  girder  bridges,  especially  in  the  United  States. 
Arches  may  be  classified  as  follows: 

(1)  Plain  arches  with  spandrel  walls,  where  the  roadbed 
rests  on  the  backfilling  or  on  masonry  not  statically  connect- 
ed with  the  arch.     These  arches  are  reinforced  by  a  double 
net  of  plain  round  rods  (Monier  system),  by  bent  beams,  or 
by  latticed  steel  arches  (Melan  system). 

(2)  Structures  in  which  the  arch  and  the  floor  construc- 
tions are  statically  connected,  used  in  Europe  under  the  name 
of  the  Wuensch  system. 

(3)  Bridges  with  ribbed  arches,  as  first  used  in  the  Henne- 
bique  system. 

In  all  three  classes  a  saving  in  dead  load  is  effected  by 
placing  cross  walls  or  columns  on  top  of  the  arches  for  the 
support  of  floor  beams  and  slabs  or  floor  arches.  Hooped 
columns  with  cross  girders,  beams  and  slabs  are  also  used  to 
save  materials  and  dead  loads. 


Fig.   92-W. 


Prof.  Greene  gives  the  following  formulas  for  Arches  with- 
out Hinges: 


BRIDGE  DESIGN  AND  CONSTRUCTION.  247 

Fig.  92-W  shows    a    symmetrical    arch-rib    loaded    vertically 
with  IV. 

Let  MI  and  M2  represent  moments  at^4and^,  respectively, 
We  have: 

H-Hi-0 


For  moment  at  any  point  distant  x  from  A,  we  get 
M=Ml  +  Vl  x—Hy  for  x  <  a 

M=Mi  +  ViX-Hy-W(x-a)         for  x  >  a 
For  vertical  shear 

V=Vi  for  .*•<<* 

V=V^—W       for^>a 

and  for  normal  stress  in  ,rib  at  x 

N  =  —  (Vsin$+Hcos$) 
J—  W  (l-a) 


Parabolic  Arch  without  Hinges.  —  Assuming  the  cross-sec- 
tion of  the  rib  to  so  vary  from  the  crown  toward  each  end 
that  at  any  section 

I=I0sec<t> 

A  =  AQsec$     (see  p.  272) 

where  70  and  AQ  denote  the  moment  of  inertia  and  cross- 
section  of  the  rib  at  the  crown  —  and  introducing  these  to- 
gether with  the  equation  of  parabola 


we  get 

H= 
where 


Mv  =  l*+12lnf>  \^(^+*hln*)-w{ (aP-6nt>)(l-aV+6l*p{>  \  1 


«2=      .     (radius  of  gyration) 


248 


REINFORCED    CONCRETE. 


where 


n  = 


4h 


and 


Neglecting   the    effect   of   axial    stress—  since    the   term 
ought  then  to  disappear,  we  get: 


_ 


and  for  temperature  stresses 


at  springing 


and 

and  neglecting  axial  stress 


and 


Mt  =  Hi  —  h      at  crown 


/"t  = 


. 

at  springing 
at  crown 


where  t  =  temperature  change  in  number  of  degrees  F. 

f  =  Coefficient  of  expansion  and  contraction. 

//t  =  Horizontal  reaction  at  the  left  support  due  to  the 
temperature  change. 


BRIDGE  DESIGN  AND  CONSTRUCTION.  249 

For  a  Parabolic  Arch  with  Two  Hinges,  we  have 


15 

and  neglecting  axial  stress,  we  get 
5a( 


L=8A2      iU 
15  +  Ah  ™ 

and  neglecting  the  axial  stress,  we  get 


For  Flat  Parabolic  Arch  with  Two  Hinges,  we  have 


i 

H=  —  —  -  W 
2  ' 


and  neglecting  axial  stresses 


„  _  Sa(l-a)  (P+al-a*)  ... 


For  full  uniform  load,  we  have  approximately 


where    w   is   uniformly   distributed   load   per   unit   length   of 
span. 

Well  proportioned  arches  of  3,  5  or  7  centers  are  drawn 
according  to  following  method. 


250 


REINFORCED    CONCRETE. 


It  should  be  borne  in  mind  that  3-center  arches  are  used 
only  for 


5-center  arches  for 


7-center  arches  for 


h  =  0.3  /to  0.36  / 


A  =  0.25  to  0.33  / 


.  92-x. 


For  3-Center  Arch.—  Strike  semicircle  with  diameter  =  J 
and  divide  same  in  3  equal  parts  at  a  and  c.  Draw  chords  and 
radii.  Select  rise  of  arch  at  B  and  draw  BA  =E  ba  and  BC  ^ 
be  intersecting  chords  from  a  and  c. 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


251 


For  5-Center  Arch.— Divide  the  semicircle  in  5  equal  parts, 
draw  chords  and  radii  and  select  the  smallest  radius  r,  thus 
determining  points  A  and  £  and  proceed  as  for  3-center  arch. 


Fig.    92-Y. 

For  7-Center  Arch  we  select   rl   and  rz.     The  following 
table  forms  a  guide  for  selection  of  these  radii : 
TABLE  LXIII-A. 


5  Centers. 

7  Centers. 

h 
/ 

TI 
~ 

h 
/ 

ri 
/ 

*"2 

~~T 

0.36 
0.35 
0.34 
0.33 
0.32 
0.31 
0.30 

.278 
.265 
.252 
.239 
.225 
.212 
.198 

.33 
.32 
.31 
•.30 
.29 
.28 
.27 
.26 
.25 

.228 
.216 
.203 
.192 
.180 
.168 
.156 
.145 
.133 

.315 
.302 
.289 
.276 
.263 
.249 
.236 
.223 
.210 

252  REINFORCED    CONCRETE. 


THE  ELASTIC  THEORY  OF  ARCHES  SIMPLIFIED.* 

Introduction. — Formerly,  when  stresses  in  plain  masonry 
arches  were  computed,  the  engineer  was  satisfied  when  the 
line  of  resistance  was  within  the  middle  third  of  the  arch 
ring,  and  this  is  satisfactory  for  symmetrical  loading  and 
heavy  voussoir  arches,  where  the  ratio  of  the  live  load  to 
the  dead  load  is  a  small  one — and  here  the  graphostatic 
method  was  considered  sufficient,  even  though  arbitrary. 

But  with  the  advent  of  reinforced  concrete  it  has  become 
necessary  to  resort  to  the  elastic  theory  to  properly  deter- 
mine the  stresses  under  symmetrical  and  unequal  loadings 
for  comparatively  light  structures,  where  temperature  stresses 
also  become  very  important. 

The  application  of  this  theory  has  not  come  into  general 
use  among  engineers,  notwithstanding  the  fact  that  experi- 
ments undertaken  by  the  Austrian  Association  of  Architects 
and  Engineers  have  demonstrated  that  arches  can  be  consid- 
ered elastic  curved  beams  and  computed  accordingly. 

While  we  admit  that  even  the  elastic  theory  does  not  give 
mathematically  correct  results,  owing  to  the  questionable 
rigidity  of  the  abutments,  a  marked  improvement  is  found 
as  compared  with  the  usual  assumption  of  three  points 
through  which  the  pressure  line  is  supposed  to  pass. 

The  designing  engineer  must  be  qualified  to  judge  as  to 
the  correctness  of  these  assumptions. 

The  method  here  given  will  in  an  extremely  simple  way 
permit  of  ascertaining  the  intensities  of  stresses  in  any  part 
of  the  arch  ring,  whether  it  be  due  to  live  or  to  dead  loads — 


*From  a  translation  by  Mr.  C.  W.  Hoffman,  C.  E.,  of  Mr.  Th. 
Landsberg's  article  in  "Zeitschrift  des  Vereins  fur  Deutscher 
Ingenieure,"  Dec.  14,  1901. 


BRIDGE  DESIGN  AND  CONSTRUCTION.  253 

and  will  also  lead  to  formulas  whereby  the  arch  ring  ma>  be 
dimensioned  in  advance  of  the  statical  examination. 

An  arch  fixed  at  both  ends  is  statically  threefold  indeter- 
minate— and  the  three  unknowns  which  cannot  be  determined 
by  the  static  theory  can  be  found  by  the  elastic  theory. 

Preliminary  Examination  of  Reactions  Caused  by  a  Con- 
centrated Load. — As  a  concentrated  load  G,  Fig.  93,  moves 
over  the  arch,  it  produces  in  each  position  two  reactions, 
7?A  and  RB ,  which  must  be  in  equilibrium  with  the  concentrat- 
ed load  G. 


Fig.   93. 

The  point  E  in  which  the  two  reactions  intersect  the  load  G 
describes  a  line,  the  form  of  which  depends  upon  the  curve 
of  the  arch  ring.  This  line  will  herein  be  called  the  "line  of 
reactions."  During  the  progress  of  the  moving  load  G  the 
two  reactions  will  envelop  curves,  which  will  be  called 
"involute  of  reactions."  The  line  of  reactions  and  the  involute 
of  reactions  being  known,  the  location,  direction  and  magnitude 
of  the  reactions  can  readily  be  found  for  any  given  position  of 
the  concentrated  load  G. 

We  will,  however,  show  that  we  can  dispense  with  the  in- 
volute of  reactions. 

If  the  line  of  reactions  is  known,  the  reactions  can  be  de- 
termined when  for  the  reactions  other  points,  A'  and  B',  Fig. 
93,  are  established,  through  which  the  reactions  must  pass 
— as  we  know  that  both  reactions  pass  through  point  E,  which 
In  turn  is  located  by  the  positions  of  load  G. 


254  REINFORCED   CONCRETE. 

Therefore  lines  passing  through  E  and  through  A'  and  B\ 
respectively,  represent  the  reactions. 

We  will  next  show  how  to  quickly  determine  the  direc- 
tion, location  and  magnitude  of  the  reactions  for  any  given 
concentrated  load  G. 

To  simplify  matters,  we  will  assume  the  arch  to  be  a  flat 
parabola,  though  the  results  can,  without  hesitation,  be  ap- 
plied to  flat  circular  arches,  or  other  curves  by  a  slight  modi- 
fication of  the  formulas. 

Let  /~span  or  horizontal  projection  of  neutral 
axis  of  arch  between  its  intersections  with  the  skew- 
back  or  springing  line 

s—  the  rise  of  the  neutral  axis. 

The  arch  is  assumed  to  be  symmetrical,  with  the  spring- 
ing lines  on  same  level.  Then  we  have  from  Fig.  94: 

(1)  The  line  of  reactions  is  a  straight  line  at  a  distance  of 
gs  above  and  parallel  to  AB. 

(2)  If  a  second  line  is  drawn  at  a  distance  of  Is   above 
and  parallel  to  AB  intersecting  the  perpendiculars  through  the 
neutral  axis  at  the  skewbacks  at  Ao  and  Bo,  then  the  lefthand 
reaction,  due  to  a  concentrated  load  at  a  distance  x  to  the 
right   from  the   center  intersects   the  perpendicular  through   A 
at  a  distance  v  below   Ao  Bo — and  the   righthand  reaction  in- 
tersects the  perpendicular  through  B  at  a  distance  if  below 
Ao  Bo',  or,  geometrically  expressed: 


-J. 


15 


The  following  simple  construction  results  (Fig.  95): 
Diaw  line  AoB0  at  a  distance  of  f  s  above  and  parallel  to  AB 
and  a  parallel  II  at  a  distance  fss  below  A0B0. 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


255 


Producing  the  load  line  G  at  a  distance  x  from  the  center 
will  cut  off  the  length  D'  D"  =  fts  between  the  parallel  lines 


..-o  Lin?  of  Reactions 


A   line   connecting  Ao   with  D"   intersects  the  perpendicular 
through  the  crown  at  L  and  we  have 

OL        A  s 


FT          7T    +    X 


OL  =  ~ ; 


A    horizontal    line    through    L    will     intersect     the    vertical 
through  A  and  A',  which  passes  through  the  lefthand  reaction. 


Fig.   95. 

The  construction  of  v'  and  B'  is  done  in  the  same  manner, 
as  is  indicated  in  Fig.  95. 


256  REINFORCED   CONCRETE. 

Connecting  these  points  with  E  gives  us  the  reactions  in 
regard  to  location  and  direction.  Their  magnitude  is  easily 
found  by  means  of  a  force  polygon. 

If  (Fig.  94)  ab  =  concentrated  load  at  E,  then 
be  =  Rt  and  ca  =  tf  . 

A  B 

Similarly,  lines  from  the  points  of  intersection  A'  and  B', 
are  drawn  for  different  positions  of  the  concentrated  load 
and  the  reactions  determined.  It  is  sufficient  to  find  these 
intersections  on  one  side  only  and  transfer  them  for  sym- 
metrical loads  to  the  opposite  side. 

Successive  Steps  in  the  Design  of  an  Arch.  —  In  computing 
an  arch  we  proceed  as  follows: 

(1)  Establish  the  arch  ring. 

(2)  Locate  point  O  in  the  perpendicular  through  the  crown 
at  a  distance  f  s  above  AB. 

(3)  Draw  the  line  A0B0  through  O  parallel  to  AB. 

(4)  Draw  a  horizontal  line  II  at  a  distance  T8gS  below  A0B0 
or  T2gs  above  A  B. 

(5)  Subdivide  the  span  AB  in  a  number  of  equal  parts. 

(6)  Establish  the   points  of  intersection  A'  and   B'  of  the 
reactions  with  the  perpendiculars  through  A  and  B  for  all  po- 
sitions  of  load  G.     (Fig.   95.) 

(7)  Draw  the  line  of  reactions  A"  B"  a  distance  f  s  above  AB. 

(8)  Lay  off  the  reactions  as  to  location  and  direction  for 
all  positions  of  load  G  by  connecting  the  points  A'  and  B'  with 
the  points  E  on  the  line  of  reactions. 

(9)  Determine  graphically  the  magnitude  of  reactions. 
This  construction  is  indicated  in  Fig.  96,  except  that  for 

the  sake  of  simplicity  the  lines  for  finding  v  and  if  have  been 
omitted. 

Line  of  Pressure  Due  to  Dead  Load.  —  Determine  weights 


for  each  point  of  loading  as  usual  (Fig.  96)  and  for  each  of 
these  loads  find  the  left  and  righthand  reaction. 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


257 


The  loads  G  are  conveniently  laid  off  at  the  points  marked 

5,  4,  3 Ill,  IV   V,  where   they  can   be   resolved   into   the 

two  reactions  which  now  are  combined  to  form  a  force  poly- 
gon, a,  h  c m,  which  hereafter  will  be  called  polygon  of 

reactions. 


Fig.  96. 

Since  all  stresses  due  to  dead  load  act  simultaneously,  all 
reactions  act  simultaneously  and  the  resulting  abutment  reac- 
tion R^  has  the  direction  a  m.  The  location  of  this  reaction  RA 

is  determined  by  an  equilibrium  polygon  5'  4'  3' II'  III' 

IV  V  with  an  arbitrary  pole  O/. 


258  REINFORCED    CONCRETE. 

The  point  of  intersection  L'  of  the  extreme  sides  of  this 
polygon  is  the  point  through  which  the  resulting  reaction, 
which  is  parallel  to  am,  must  pass. 

Combining  7?A  with  G*>  G± the  line  of  resistance  and  the 

line  of  pressure  can  be  drawn,  as  shown  in  Fig.  96. 

It  will  be  noted  that  this  construction  is  free  from  ar- 
bitrary assumptions — and  we  can  easily  check  the  location 
of  point  m,  as  the  vertical  component  of  am  must  be  equal  to 
one-half  of  the  total  vertical  load. 

Line  of  Pressure  for  the  Critical  Condition  of  Loading. — 
We  will  demonstrate  later  how  to  determine  the  critical  po- 
sition of  the  live  load  for  any  section;  for  the  present  be 
it  assumed  that  these  positions  are  known. 

Then  determine  the  amount  of  live  load  which  under  most 
unfavorable  conditions  will  come  upon  each  point  of  loading 
— that  is,  a  load  Le,  where  L  equals  live  load  per  lin.  ft.  and  e 
the  distance  between  assumed  points  of  loading. 

This  load  is  then  consecutively  placed  on  all  points  of 
loading  and  the  resulting  reactions  are  determined  as  in  Fig. 
96  and  combined  to  form  the  left  (right)  hand  reaction  poly- 
gon; then  draw  the  equilibrium  polygon  with  the  arbitrary 
pole  O.  In  Fig.  97  a  b  c m  represents  the  reaction  poly- 
gon and  O2  the  pole. 

The  equilibrium  polygon  is  marked  V" ,  IV",  III",  II",  I", 
1",  2",  3",  4",  5".  With  these  two  polygons  the  corresponding 
line  of  pressure  for  any  condition  of  loading  can  be  deter- 
mined. 

Let  it  be  assumed  arbitrarily  that  in  order  to  produce 
maximum  stress  in  Joint  2  the  points  7,  II,  III,  IV,  V  would 
have  to  be  loaded.  The  loads  I,  II,  III,  IV,  V  produce  a  re- 
action on  the  lefthand  side,  the  magnitude  and  direction  of 
which  are  represented  by  fm  in  the  reaction  polygon.  The 
location  is  determined  by  the  condition  that  the  resultant 

fm  =  Rl_v 

must  pass  through  the  intersection  of  those  sides  of  the  equilib- 
rium polygon  which  border  the  forces  Rl  and  RV  that  is,  point  a. 

Combining  R^    with  the  reaction  caused  by  the  dead  load 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


259 


in  Joint  2  gives  us  the  total  resultant  due  to  this  condition  of 
loading  and  acting  at  Joint  2. 

This  force  was  determined  in  regard  to  location,  direction 
and  magnitude  under  the  head  of  line  of  pressure  due  to  dead 
loads. 


Fig.  97. 

Assuming  now  that  the  maximum  stress  in  Joint  2  would 
occur  when  points  5,  4  and  3  were  loaded,  the  procedure 
would  be  similar  to  that  just  illustrated. 

The  lefthand  reaction  R:>.^  is  first  determined  as  to  location, 
direction  and  magnitude,  and  combined  with  the  loads  to  the 
left  of  Joint  2,  t.  e.,  with  the  loads  at  points  5,  4,  3.  The"  re- 
sultant R  intersects  Joint  2  at  5,  and  is  finally  to  be  combined 
with  the  reaction  due  to  the  dead  load. 


260  REINFORCED    CONCRETE. 

It  is  clear  that  by  this  method  the  critical  position  of  the 
line  of  pressure  and  its  deviation  from  the  neutral  axis,  as 
well  as  the  intensity  of  stress  for  any  section  of  the  arch 
ring  can  be  found,  provided  the  most  unfavorable  condition 
of  loading  is  found. 

Critical  Condition  of  Loading  for  a  Given  Section, — The 
reactions  due  to  a  moving  concentrated  load  at  once  dis- 
close the  most  unfavorable  condition  of  loading,  so  that  the 
involute  of  reactions  may  be  dispensed  with. 

Considering  the  points  near  the  intrados  of  a  section, 
then  any  force  in  this  section  passing  above  the  middle  third 
produces  tension  at  the  intrados;  any  force  in  the  section 
passing  below  the  upper  limit  of  the  middle  third  produces 
compression  at  the  intrados. 

For  points  of  loading  at  the  right  of  the  assumed  sec- 
tion under  a  moving  concentrated  load,  the  lefthand  reac- 
tion is  determinate  and  for  points  of  loading  at  the  left  of 
the  section,  we  must  consider  the  righthand  reaction. 

We  recommend  that  both  right  and  left  reactions  be 
drawn. 

However,  if  the  reactions  for  but  one  side  are  drawn, 
the  opposite  reactions  may  be  examined  in  a  section  located 
symmetrically  with  the  one  under  investigation — letting  the 
reactions  act  there. 

In  Fig.  97  the  lefthand  reaction  at  section  3  for  a  con- 
centrated load  at  point  2  accidentally  passes  through  K»,  the 
tipper  limit  of  the  middle  third,  but  the  reactions  due  to  a  load 
in  1,  I,  II,  III V,  intersect  below  the  middle  third,  produc- 
ing compression  near  the  intrados  at  section  3,  while  a  load 
at  point  3  produces  tension  at  these  points. 

In  order  to  find  the  stress  produced  by  a  load  in  4  and  5 
(at  the  left  of  3)  we  investigate  section  ///  with  reference  to 
the  effect  of  a  load  at  IV  and  V.  A  load  at  4  and  5  will  have 
the  same  effect  on  section  ///. 

We  see  that  loads  at  IV  and  V  produce  tension  at  the  in- 
trados of  section  ///  because  the  reactions  Rly  and  Rv  pass 
the  section  far  above  the  middle  third. 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


261 


Maximum  tension  in  section  3  therefore  is  found  by  load- 
ing points  5,  4  and  3,  maximum  compression  is  found  by 
loading  points  2,  1,  /,  //., V,  while  a  load  at  point  2  pro- 
duces a  stress  equal  to  zero. 

It  is  sufficient  to  consider  the  points  on  one  side  of  a 
section  as  fully  loaded  and  the  points  on  the  other  side  as 
not  loaded. 

Proof  of  the  Correctness  of  Locating  Points  A'  and  B'. — 
If,  according  to  Muller-Breslau  (Die  neueren  Methoden  der 
festigkeitslehre,  2d  edition,  p.  115),  the  two  forces  X  and  Y, 
acting  at  O  and  the  moment  Z  be  considered  as  the  three  un- 
known quantities,  then  X  can  be  found  from  the  condition  that 
the  algebraic  sum  of  the  moments  of  X  and  Y  and  of  the  mo- 
ment Z  with  the  point  A  as  a  center  must  be  equal  to  the  re- 
sisting moment  at  the  springing  or  skewback  A,  Fig.  98. 


The  origin  O  must  be  so  chosen  that  in  each  of  the  three 
equations  for  elastic  arch  all  unknowns  are  eliminated  but 
one.  With  this  in  view  the  point  O  must  represent  the  center 
of  gravity  of  the  neutral  axis,  and  X  and  Y  must  coincide  with 
the  two  principal  axes  of  the  arch  center  line.  If  the  latter  is 
a  flat  parabola  with  a  nse  =  ,y  and  a  span  =  /,  the  point  O  will 
be  located  at  a  distance  $s  above  AB. 

Assuming  a  load  at  a  distance  x  to  the  right  of  the  center, 
we  may  write  the  three  following  equations: 


(25) 


262 


REINFORCED    CONCRETE. 


By  means  of  Formulas  (25)  the  influence  lines  for  the  three 
unknown  quantities,  X,  Y  and  Z,  can  easily  be  drawn.  For  two 
positions  of  the  load  symmetrical  with  respect  to  the  vertical 
axis,  X  and  Y  have  equal  values.  Y  changes  its  sign  with  x, 
hence  symmetrical  positions  of  Y  only  change  the  sign. 

Uniform  load  equal  on  both  sides  of  the  center  makes 
7  =  0. 

In  order  to  replace  X,  Y  and  Z  by  their  resultant,  we  com- 
bine the  resultant  of  X  and  Y  with  the  moment  Z,  which  causes 
a  parallel  shifting  of  the  resultant  of  X  and  Y.  Since  its  di- 
rection is  given  by 

Y 
tan  8  =  -j£ 

it  will  be  sufficient  to  establish  one  point  through  which  it 
must  pass. 

Assuming  that  the  resultant  intersects  the  vertical  center 
line  at  S,  a  distance  m  below  O,  then  the  algebraic  sum  of  the 
static  moments  of  X,  Y  and  Z  must  equal  zero;  that  is,  the  fol- 
lowing equation  for  m  must  be  satisfied: 


Fig.  99. 

£ 

X  m  —  Z  =  0,  whence  m  =  -y 

Substituting  the  values  of  Formulas  (25)  for  X  and  Z, 


The  resultant  passing  through  5  forms  the  angle  5  with  the 
horizontal,  and  if  the  negative  sign  of  Y  is  taken  care  of  by 
laying  it  off  downwards,  we  have 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


263 


Y  32sx 

=  X  =  15  (J2  - 


and  with  the  relations  in  Fig.  99, 

I 
u  =      tan  5  = 


IQslx 


m  —  u  = 


At  point  ^4i  the  resultant  of  X,  Y  and  Z  is  combined  with  the 
vertical  component  of  the  left  hand  abutment  reaction. 

The  reaction  we  find  (Fig.  100),  therefore,  must  pass 
through  Ai.  When  the  load  advances  to  the  left  of  the  center 
line  we  obtain  similarly, 


Fig.  100. 


m  = 


8sP 


IGslx 


l  =  15  (P  —  4*2) 

Particular  notice  must  be  given  to  the  fact  that  MI  is  posi- 
tive when  laid  off  downwards  while  u  is  positive  when  laid 
off  upwards. 

By  addition  we  obtain 

8sl 


The  values  for  v\  hold  good  for  loads  at  the  right  of  the 
center  for  righthand  reactions,  and  the  values  v  for  righthand 
reactions  when  the  load  is  at  the  lefthand  side  from  the 
center. 

Approximate  Analysis  of  Dead  Load.  —  In  the  following 
investigation  we  assume  the  upper  limit  of  the  dead  load 
diagram  to  be  a  straight  line,  as  shown  in  Fig.  101,  the  in- 


264 


REINFORCED    CONCRETE. 


trades  to  form  a  parabola,  the  rise  of  the  arch  to  be  s  and  the 
height  of  the  dead  load  diagram  at    center  equal  to  r. 

At  any  point  a  distance  x  from  the  center  the  height  of  the 
dead  load  diagram  is 


r  + 


4s*2 


or  with  a  weight  per  unit  of  D  the  load  over  dx  is 

(4sx2\ 
r   +  -p-J  dx 


t= 


Fig.  101. 


For   this    condition   of   loading    Formulas    (25)    furnish    the 
following  values: 


....  (26) 


81 


BRIDGE  DESIGN  AND  CONSTRUCTION. 
or  when  integrating, 


265 


KD=0 


DP 
=  60  <5r 


(27) 


Since  VD  =  0,  the  resultant  from  XD  and  YD  is  acting  hori- 
zontally, and  is  of  the  magnitude  XD ,  intersecting  the  vertical 
center  line  at  a  point  mD  below  O. 

We  have 


0,  or  m. 


Referring  to  Formulas  (27),  we  get 


X, 


8 


always  intersects  the  vertical  through  the  springing  line 


at  a  distance  mD  below  O. 


The  resultant  of  all  forces  acting  at  the  left  (or  right)  of 
the  crown  intersects  the  vertical  center  line  at  a  distance  above 
O,  which  is  equal  to  n  and  subject  to  the  following  conditions 
(Fig.  102): 


Fig.  112. 


266  REINFORCED    CONCRETE. 


10r 


The  point  of  intersection  between  the  resultant  and  the 
center  line  is  located  at  a  distance  X  below  the  neutral  axis  ai 
the  crown,  and  we  have 


The    abutment    reaction    intersects    the    vertical    through 
the  springing  at  a  distance  w  below  the  axis  AB,  and  we  have 


w  =  m    — 


The  intercepts  between  the  neutral  axis  and  the  lines  of 
pressure  are,  at  the  crown,  downward, 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


267 


at  the  springing,  downwards, 


IV  *=  T5 


TABLE  LX. — VALUES  OP  X  AND  w  FOR  VARIOUS  VALUES  OP  — . 


5 

f 

1 

1.5 

2 

2.5 

3 

4 

X 

0.01255 

0.0185 

0.02s 

0.026s 

0.03s 

0.036s 

W 

0.0335 

0.0475 

0.065 

0.067s 

0.07s 

0.093s 

With  these  three  points,  the  location  of  the  line  of  pres- 
ure  and  the  intensities  of  stress  on  any  part  of  the  arch  ring 
are  established. 

Thickness  of  Arch  Ring  at  Crown  and  Springing. — The 
course  of  investigation  is  as  follows: 

The  condition  of  loading  which  is  most  unfavorable  at 
the  crown  is  determined,  and  as  the  line  of  pressure  due 
to  the  dead  load  deviates  downwards,  it  is  obvious  that  such 
position  of  the  live  load  as  will  make  the  pressure  line  de- 
viate still  further  is  especially  unfavorable.  For  a  given 
load  this  position  of  the  live  load  can  be  easily  determined 
by  drawing  a  tangent  to  the  involute  of  reactions  passing 
through  the  upper  limit  of  the  middle  third  of  the  ring  at 
the  crown  (Fig.  103).  Their  intersections  L?  and  L"  with  the 
Jine  of  reactions  indicate  the  points  to  which  the  live  loads 


REINFORCED    CONCRETE. 


must  advance.  All  loads  at  the  left  and  right  of  points 
L'  and  L"  produce  compression  in  the  parts  of  the  crown  near 
the  intrados. 

In  order  to  obtain  the  maximum  stresses  this  space  must 
be  completely  covered  by  the  live  load. 

For  approximate  calculations  we  may  assume  that  L'L" 
represents  the  middle  third  of  the  span  and  the  two  outer 
thirds  are  supposed  to  be  under  a  live  load  L  per  lin.  ft. 

Then  we  have,  according  to  Formulas   (26), 
,  Line  of  ReacJ-'ions  or  Locus 


t_ 


Fig.  103. 


2  x  15 


—  4#2)2  dx  =  —-—-  (approximately) 


(28) 


x=  —  (approximately  ) 

The  intersection  of  X,  Y,  Z  with  the  vertical  center  line  is 
located  WL  below  O  (Fig.  104),  and  we  have 
XT  w—  Z,=  0 

L        L  L 

_LZ_2      645 
mL  ~  24  '    3LZ2  ~  »5 
The  resultant  XL  intersects  the  vertical  axis  at  a  distance  of 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


269 


The  resultant  of  the  forces  acting  on  one  side  of  the  ver- 
tical axis  intersects  same  at  a  point  located  a  distance 
t  below  the  crown,  t  being  found  as  follows: 


Fig.  104. 


3LI* 


645 


or 


LZ2       645 


3      6 
X,   = 


'  =  *(  V  -  !f)  =  2P7 

The  resultant  of  all  forces  on  one  side  of  the  vertical  axis 
—  dead  load  and  live  load  —  intersects  the  joint  at  the  crown 
at  a  point  T  (Fig.  105).  The  location  of  point  T  is  as  follows: 


Fig.  105. 


X 


X, 


•*£ 


270 


REINFORCED   CONCRETE. 


S   is  the   maximum   deviation   at  the   crown   and   is   figured 
positive  downwards. 

If  we  simplify  matters  by  making 


21 


and 


—  we  have  C  =        nr 
5  8     — 


L 


C     s  C  I 

-    27_X    +  27  =  *  U  =  27 


+    C 


or  approximately 


27 


For 


These  values  are  shown  in  Table  LXI. 

TABLE  LXI. — VALUES  OF  C,  X  AND  S'  FOR  VARIOUS  VALUES  OF  — . 


5 

r 

i 

1.5 

2 

2.5 

3 

4 

C 

0.492 

0.772 

0.875 

1.036 

1.180 

1.432 

X 

0.01255 

0.0185 

0.025 

0.0265 

0.035 

0.0365 

S'j 

0.0125* 
+  0.0182 

0.0185 
+  0.0286 

0.025 
+  0.0324 

0.026s 
+  0.0384 

0.03? 
+  0.0437 

0.0365 
+  0.0530 

The  maximum  intensity  of  stress  Sm  at  the  crown  occurs 
at  a  deviation  5"  of  the  resultants  from  the  neutral  axis.  Ii 
the  thickness  of  crown  =  d,  we  have 


BRIDGE  DESIGN  AND  CONSTRUCTION.  271 


C          _ 

where  X          =  X     +  X 


L 

If  K  denotes  the  maximum  permissible  unit  stress,  we  have 
the  following  equation  for  d, 

d  65 

*  K~ 


2K 
hence, 

_Dl* 

_DP 
If  we  assume 


~ 


we  have 
and 


Y 

A(D+L)     "-     85 


For  convenience  we  will  here  repeat  the  notation  in  above 
formula: 

d  =  thickness  of  crown  in  feet. 
D  =  weight  per  cu.  ft.  of  masonry  in  Ibs. 
/  =  span  of  neutral  axis  in  ft. 
.y^rise  of  neutral  axis  in  ft. 

/£  =  permissible  pressure  on  masonry  in  Ibs.  per  sq.  ft. 
r  =  height  at  crown  of  dead  load  diagram  in  ft.   (Fig.  101). 
L=:live  load  in  Ibs.  per  sq.  ft. 


272 


REINFORCED    CONCRETE. 


Example. — Find    thickness   of   crown    in    parabolic    arch    for 
the   following   conditions: 

I  =  60,  5  =  6,  r  =3,  L  =  100  Ibs.  D  =  150  Ibs. 


We  have  then  —  =  TJ- 


2,  K  =  144  X  400  =  57,600  Ibs.  sq.  ft. 


hence 


S  =  0.025  +  0.0325 


=  0.1525 
=  4.11. 


From  Formula  (29)  , 
4.11  X  150  X  602 


2  l^          I 
6  I1  +  V 


1  + 


192  x  0.1525  X  57,600  X 


16   X   57,600  X  6  \A   r  \  A  4.11  x  150  x  602        / 

=  1.334  ft.  for  a  plain  concrete  arch. 

Thickness  of  Arch  Ring  on  Both  Sides  of  Crown  Down 
to  the  Skewback. — A  quick  and  practical  method  of  finding 
the  thickness  of  the  arch  at  any  point  after  finding  the  crown 
thickness  is  as  follows  (Fig.  106) : 


Fig.    106.    —    Diagram    Showing       Fig.  107. — Diagram  Showing  Lo- 
Method  of  Finding  Thick-  cation  of  Neutral  Axis, 

ness    of   an   Arch. 

(1)  Draw   radial   lines   dd   intersecting  the   neutral   axis   at 
right    angles,    and    perpendicular    lines    through    the    points    of 
intersection. 

(2)  On  these   perpendicular   lines   lay  off  the   crown   thick- 
ness ab  and  produce  horizontally  to  the  radial  lines  dd,  cutting 
them    at  points   c.     Then    the   distances   cc   represent   the   arch 
thicknes-s  at  the  various  points. 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


273 


Location  of  Neutral  Axis.  —  According  to  Prof.E.  Moersch 
in  "Der  Eisenbetonbau,"  1906,  we  have  the  following  equation 
for  the  location  of  the  neutral  axis,  p  being  the  percentage  of 
reinforcement  on  each  side  of  the  neutral  axis  (Fig.  107)  : 


Making  e  =  OA2d  and  Fe  =  pbd,  we  have 

M_        -x3  +  \dx*  +  31.75ft 
N~d~ 

Here  N  = 

hence 


_M  _5 
Nd  —  d 
The  curves,  Fig.    108,  are    plotted    for    values  of  x  =  O.ld; 

0.2d,  0.3d,  etc.,  as  abscissas  and  j  for  different  percentages  of 
reinforcement  p  =  0.001,  p  =  0.002,  p  =  0.003.,  etc.,  as  ordinates. 


Fig.  108.— Diagram  of  Curves  for  Different  Values  of  P. 

When  x  is  found  either  by  trial  from  Fcrmula  (41)  or  taken 
from  the  diagram,  Fig.  108,  the  different  stresses  are  found 
as  follows  (Fig.  107): 


274  REINFORCED    CONCRETE. 


(32) 


c  W 

or  ob  =  • 

bx_      fcn  ,2x—d)  " (32a) 

where  fc  is  the  reinforcement  at  either  extrado  or  intrado 
providing  they  are  alike. 

Tension:  5e  =  «5b ~ =  15Sb  °-92^~-r (33) 

X  X 

Compression:    6V=  156"b  ~~  ~    (34) 

where  j*-  =  15 

Thermal  Stresses. — According  to  Prof.  Cain,  the  thermal 
stresses  in  a  reinforced  concrete  arch  ring  may  be  expressed  as 
follows : 

TT  Ec  let          7C  —  nls  /Qr, 

ti.   =  ~^r~, ^ ^r~7 r        c.       (oo) 

2,  {y^)  —  m  Z  \y)         o 

where 

H  =  the  horizontal  thrust  at  the  crown  due  to  change  of  the 
length  of  the  arch  line  with  change  of  temperature, 

t  =  degrees  change  in  temperature, 

e  =  expansion  per  degree. 

a 

a  =  number  of  segments,  s,  in  the  arch  ring, 
/  =  span, 

y  =  the  ordinates  of  s. 

The  normal  force  at  any  joint  will  be  the  component  of  H 
perpendicular  to  that  joint,  and  the  bending  moment  will  be 

Buel  &  Hill  give,  p.  136  of  Reinforced  Concrete, 

=  DEC  (/c  +  «/•)  (36) 

ss  (xy) 

where  D  —  deflection  at  crown  due  to  change  of  length  of  arch 
ring  with  changes  of  temperature  and  H  the  corresponding  hori- 
zontal thrust. 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


275 


By  tabulating  the  values  xy  for  all  the  segments  s  of  the 
ring  from  one  springing  to  the  other,  the  solution  is  quite 
simple,  since 

Ec  (7C  4-  n/B).  . 

— - —    —  is  constant. 

Prof.  Cain*  suggests  that  an  increase  of  steel  should  be  used 
in  arches  to  satisfy  the  condition  at  any  critical  point,  that  all 
the  bending  moments  due  to  load  and  temperature  should  be 
borne  entirely  by  the  steel  at  some  stress  under  the  elastic  limit, 
say  20,000  Ibs. 

EXAMPLE  OF  AN  ARCH  DESIGNED  ACCORDING 
TO  THE  ELASTIC  THEORY. 

Assumptions. — In  a  bridge  of  84  ft.  span,  having  a  rise  of 
10  ft.  6  ins.,  we  have  a  live  load  of  250  Ibs.  per  sq.  ft.,  a  6-in.  earth 
fill  at  the  crown  and  a  12-in.  pavement.  Thickness  of  arch  ring 
is  assumed  to  be  14  ins.  at  the  crown  and  20  ins.  at  the  springing. 
To  find  r  we  have,  reduced  to  concrete  weight : 

1.167  ft.  concrete  at  150  Ibs.  per  cu.  ft.  =  1.167 
6  in.  earth  fill  at  120  Ibs.  per  cu,  ft.        =  0.4 
12  in.  pavement  at  150  Ibs.  per  cu.  ft.    =  1.0 

r  =  2.567  ft. 
/  =  84ft. 
s  =  10.5  ft. 
r  —  2.567  ft. 

Constructing  the  Arch  Ring. — Assuming  a  parabolic  arch, 
the  ordinates  are  conveniently  found  by  using  the  formula : 


(37) 


1      14      21      &      35 


Fig.    109.— Parabolic  Arch-Ring   for  84-Ft.    Arch. 
*  Theory  of  Concrete  Steel  Arches  (p.  79). 


276 


REINFORCED    CONCRETE. 


One-half  the  span  is  divided  into  12  equal  parts,  each  3.5  ft. 
long,  as  shown  in  Fig.  109.  The  values  for  y  are  shown  in  Table 
LXII.  The  ordinates  3;  of  the  parabola  are  checked  by  their  dif- 
ferences as  shown,  the  second  difference  being  a  constant. 

TABLE  LXII. — ORDINATES  OF  PARABOLA  WITH  VARIOUS  VALUES  FOR  x. 


Values  of  x. 

Values  of  y. 

First 
difference 

Second 
difference. 

Q      K 

4X10.5 

O    C     /  O  4           O     C\ 

1    A77 

#=  O  .  0 

y  —             o.o  (o$     6.0) 

84  » 

=      1,9  f  4 

1.531 

x=7. 

y=  7(84-7) 

=    3.208 

0.146 

168 

1.385 

1 

*=10.5 

y  =  10.5(84-10.5) 

=    4.593 

0.145 

168 

1.240 

1 

*=14. 

y  =  14(84-14) 

-    5.833 

0.146 

168 

1.094 

1 

*=17.5 

y  =  17.5(84-17.5) 

-    6.927 

0.146 

168 

0.948 

1 

*=21. 

y  =  21  (84-21) 

=    7.875 

0.146 

168 

0.802 

*=24.5 

y  =  24.5(84-24.5) 

=   8.677 

0.146 

168 

0.656 

1 

*=28. 

y  =  28  (84-28) 

=   9.333 

0.145 

168 

0.511 

1 

*=31.5 

y  —  31.5(84-31.5) 

=    9.844 

0.147 

168 

0.364 

1 

x  =  35. 

y  35(84-35) 

=  10.208 

0.145 

168 

0.219 

1 

*=38.5 

y-  38.5(84-38.5) 

=  10.427 

0.146 

168 

0.073 

1 

*=42. 

:,  =  42(84-42) 

=  10.5 

168 

BRIDGE  DESIGN  AND  CONSTRUCTION.          277 

Dead  Load  Diagram. — Next  the  dead  load  ordinates  are 
reduced  to  concrete  weights  by  multiplying  by  Jfg  and  the 
dead  load  line  drawn.  The  lengths  of  the  center  lines  of  the 
panels  are  as  follows: 

Ca  =  10  ft.  2  ins. 

GV=7  ft.  8  ins. 

G4  =  5  ft.  9  ins. 

£3  —  4  ft.  3  ins. 

£2  =  3  ft.  3  ins. 

d  =  2  ft.  9  ins. 

The  panel  loads  are  found  as  follows : 

Go  =  10%  X  7  X  150  =  10,700 

G5  =  7%  X  1050  =  8,000 

C4  =  5%  X  1050  =   6,000 

£3  =  4}i  X  1050  =   4,500 

£,=1314  x  1050  =  3,400 

G,  =  2%  X  1050  =  2,900 

Total  dead  load  on  half  span  =  35,500  Ibs. 

We  have  s  =  10.5,  hence  $s  =  7  ft.  and  T«ss  =  5.6  ft., 
locating  lines  A0  B0,  /-/  and  A"  B"  in  Fig.  110.  The  line  A"  B" 
incidentally  coincides  with  the  reduced  load  line.  The  force 
triangles  are  next  drawn,  combining  each  two  reactions  with  the 
panel  loads,  and  the  reaction  polygon  is  plotted  and  checked  by 
finding  its  vertical  ordinate  equal  to  35,500  Ibs.  or  the  half  span 
dead  load. 

The  pressure  line  is  next  transferred  to  the  arch  from  the 
equilibrium  polygon,  and  we  find  that  for  the  dead  load  alone, 
the  pressure  line  deviates  considerably  from  the  center  line  of 
the  arch,  which  therefore  in  practice  would  be  modified  to  coin- 
cide more  closely  with  the  line  of  pressure.  With  the  adoption 
of  a  new  center  line,  the  same  calculations  would  have  to  be 
repeated.  In  the  present  example,  however,  the  original  center 
line  has  been  adhered  to. 

The  rays  0-6  0-5 O-l,  in  Fig.  110,  represent  the  forces 

acting  at  joints  6,  5  ....  0  measured  in  the  scale  of  forces.  The 


278 


REINFORCED    CONCRETE. 


BRIDGE  DESIGN  AND  CONSTRUCTION.  279 

intercepts  between  the  line  of  pressure  and  the  center  line  of  the 
arch  are  their  levers  measured  perpendicular  to  the  center  line 
and  in  the  dimension  scale  of  inches. 

It  must  be  noted  that  the  forces  acting  at  the  joints  when 
taken  from  the  force  polygon  will  not  intersect  the  joints  at  right 
angles.  To  obtain  the  normal  forces  ND  we  must  multiply  the 
polygon  forces  by  the  cosine  of  the  angle  which  they  form  with 
the  perpendicular  to  the  joints.  This  is  done  simply  by  project- 
ing them  graphically. 

These  normal  forces  N0 ,  their  levers  S  and  the  correspond- 
ing moments  all  due  to  dead  load,  are  found  in  table  LXIII, 
where  they  will  be  combined  with  the  moments  due  to  live  load 
in  order  to  find  the  maximum. 

Live  Load  Diagram. — The  live  load  was  assumed  to  be  250 
Ihs.  per  sq.  ft.,  hence  the  load  for  a  panel  3.5  ft.  in  length  and  1 
ft.  depth  is  250  X  3.5  X  1  =875  Ibs. 

Three  different  positions  of  loading  will  be  considered  in  this 
example,  namely: 

(1)  Arch  completely  covered  with  live  load. 

(2)  Arch  one-half  covered  with  live  load. 

(3)  One-third  arch  from  each  end  covered  with  live  load. 

(1)  The   right  and  left   hand    reactions   for   a  concentrated 
moving  load  are  first  determined  and  combined  to  form  the  re- 
action polygon,  and  then  the  line  of  pressure  drawn  exactly  as 
described  for  dead  load. 

The  values  of  A/"L  (normal  pressure  at  joints  due  to  live  loads) 
and  their  levers  at  the  several  joints  are  scaled  off  from  the 
diagram.  Fig.  Ill,  and  their  values  recorded  in  Table  LXIII, 
together  with  the  resulting  moments. 

The  line  of  pressure  is  symmetrical  about  the  center  and  has 
been  plotted  for  one-half  of  the  arch  only. 

(2)  When  the  arch  is  covered  with  live  load  over  one-half 

the  span  only  the  forces  (J<. G\  are  acting.      The  resultant 

reaction   R^\    due   to  this   condition  of  loading  passes   through 
point  C,  which  is  the  intersection  of  the  sides  6  and  0  in  the 
equilibrium  polygon.    With  the  direction  and  location  of  the  left 


280 


REINFORCED    CONCRETE. 


BRIDGE  DESIGN  AND  CONSTRUCTION.  281 

hand  reaction  given,  the  line  of  pressure  due  to  this  condition 
of  loading  is  easily  drawn  as  shown  in  the  live  load  diagram, 
Fig.  111. 

(3)  The  line  of  pressure  for  the  arch  when  covered  with  live 
load  on  the  two  outer  thirds  is  found  when  the  loads  Ge  6rB  G«  Gz 
and  Gm  Glv  Gv  Gyl  are  acting.  The  construction  is  similar 
to  the  one  described  and  the  line  of  pressure  is  symmetrical  about 
the  center  of  the  arch,  therefore  only  one-half  is  drawn  in  the 
diagram.  The  resulting  normal  forces  and  their  levers  are  again 
scaled  off  and  with  their  corresponding  moments  plotted  in 
Table  LXIII. 

Maximum  Fiber  Stresses. — An  examination  of  Table 
LXIII  readily  gives  the  maximum  moments  due  to  the  four 
conditions  of  loading  at  any  joint,  and  when  added  they  will  give 
the  maximum  at  the  joint  in  question.  These  maximum  figures 
are  underlined  in  the  tables. 

It  will  be  noticed  that  the  moments  due  to  dead  load  are  by 
far  the  greatest,  while  the  moments  due  to  full  live  load  over  the 
entire  arch  do  not  produce  maximum  stresses  in  any  joint. 

From  Table  LXIII  we  determine  the  fiber  stresses. 

The  percentage  of  reinforcement  at  the  crown  is  assumed  as 
p  =  1  per   cent  =  0.01   for  extrados  and   1  per  cent   for  the 
intrados.    The  same  size  of  reinforcement  is  maintained  through- 
out the  arch,  hence  the  percentage  at  the  springing  is 

p  =  1  per  cent  X  f$  =  0.007 

The  stresses  produced  in  each  joint  we  have  learned  are  due 
to  a  normal  force  N  and  a  moment  M,  and  they  are  figured  un- 
der the  usual  assumption  that  the  stress,  and  consequently  the 
deformation  in  any  fiber,  is  directly  proportional  to  its  distance 
from  the  neutral  axis,  so  that  a  section  which  is  plane  before 
bending  remains  plane  after  bending.  The  distance  x  of  the 


282 


REINFORCED    CONCRETE. 


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.  .  (40) 

BRIDGE  DESIGN  AND  CONSTRUCTION.  283 

neutral  axis  from  the  compressed  fiber  is  found  by  Formula  (30), 
which  for  the  sake  of  convenience  we  write 


where 


C  =  -Gnpd  (-fid  +  2fc2j   ...........  (41) 

We  solve  x  by  trial,  or  for  n  =  15  it  may  be  taken  direct 
from  Fig.  108,  and  inserted  in  Formulas  (32),  (33)  and  (34), 
where 

Sb  ==  compression  in  extreme   fiber  of  concrete  in  Ibs.  per 

sq.  in. 

Se  =  compression  in  steel  in  Ibs.  per  sq.  in. 
5e'  =  tension  in  steel  in  Ibs.  per  sq.  in. 

As  before  stated,  the  moments  in  Table  LXIII,  and  therefore 
the  unit  stresses,  could  be  considerably  reduced  if  the  line  of 
pressure  found  for  dead  load  had  been  chosen  for  a  new  arch 
ring. 

A  spandfel  construction  would  also  reduce  the  dead  load 
stresses  to  a  considerable  extent. 

A  diagram  like  Fig.  108  can  readily  be  prepared  for  »  =  20 
instead  of  n  ==  15. 

Moments,  Stresses,  etc.,  at  the  Crown.  — 
M  =  256,690  inch  Ibs. 
N   •=  52,230  Ibs. 
d    =  14  ins. 
n    =  20 
p    =  0.01 
e    =  0.42J 
Substituting  in  Formulas  (39),  (40)  and  (41), 

Id        M\  /14       256690 

A  -   -3~~  =  ~3~ 


52230 


\ 

;=   -6' 


M  256690 


B  =  12-ft-npd=  12  5223Q  20  X  0.01  X  14  =  165.0 


284  REINFORCED    CONCRETE. 

C   = 


[256690 
5223Q    14  +  2  (0.42  X  14)2J   =    -2314.7 

Hence  we  have,  substituting  in  Formula  (38), 
x3  -  6.27*2  +  165*  —  2314.7  =  0 
which  gives  *  =  10.8 

(Using  Fig.  108  for  n  =  15,  we  would  have 

S  =  jj-  =  4.91,  j  =  -jj-  =  0.35  and  *  =  0.74d  =  10.36) 

Substituting  in  Formulas  (32),  (33)  and  (34), 

2Nx  2X52,230X10.8 


*~  bx*+2pbdn(2x-~d)  "  12X10.82+2X0.01X  12X14X20(2X10.8-  14) 
=*  591  Ibs.  per  sq.  in. 

Se  =  ttSb  —  =  20  X  591  -       10  g~      =  2269  Ibs.  per  sq.  in 

x  —  Q.OSd  10.8-0.08x14 

Se'  =  nSb  -    —  -=20x591-    —    -—    ~  =    10,591    Ibs.   per 


sq.  in. 
Moments,  Stresses,  etc.,  at  the  Springing.  — 

M  =  623,800  inch  Ibs. 
N  =  61,900  Ibs. 
d     =  20  ins. 
n    =  20 


14 
p    = 

Hence 


—  X  0.01  =  0.007. 


20        623800 


/  623800  \ 

B  =    12  (   G1900   20  X  0.007  X  20  )  =  338.6. 

(/>r>oQr\r\  \ 

61900   20  +  2  x  8-42)    =    -5757.7 
xs  +  0.23*2  +  338.6*  —  5757.7  =  0 
from  which  x  =  11.9 


BRIDGE  DESIGN  AND  CONSTRUCTION.  285 

(Using  Fig.  108  for  n  =  15,  we  would  have 
S  =  -rr  =   10.08,  -r  =  — T^T  =  0.5  and  x  =  0.565d  =  11.3  ins.) 


Substituting  as  before,  we  have 

2  X  61900  X  11.9 


754  lbs.f 


12  X  11. 92  +  2  X  0.007  X  12x20x20(2x11. 9-  20) 
per  sq.  in. 

Se    =  20  X  754  — '    n  ~  =  8,234  Ibs.  per  sq.  in. 

11  9-0.08  X  20 
Se'   =  20  X  754  -         n  Q        -  =  13,044  Ibs.  per  sq.  in. 

Moments,  Stresses,  etc.,  at  Joint  4. — 

M  =  320,200 
N  =  55,300 

d    =  18 

p    =  —  x   0.01  =  0.00778 

n    =  20 
A    =  -9.63 
B    =  194.4 
C   =  -3671.1 

xs  _  9.63*2  +  194.4^  —  3671.1  =  0 
which  gives  x  =  14.2 

(Using  Fig.  108  for  n  =  15,  we  would  have 

5  =^-=  5.79,  j  =   fg-  =  0.322  and ^=0.757^=13.6  ins.) 

Therefore 

2  X  55300  X  14.2 

5b    =  12  X  14.22  +  2  X  0.00778 X  12  X  18  X  20(2  X  14.2 -  18)  " 
per  sq.  in. 

0.92  X  18—  14.2 
Se    =  20  X  504  -      ~J4~2 —     ""  =  1675  lbs<  per  sq*  *n* 

14.2  —  0.08  X  IS 
Se'  —  20  x  504 -g =  9058  Ibs.  per  sq.  in. 


286 


REINFORCED    CONCRETE. 


Construction  of  Arch  Centering. — The  centering  employed 
for  a  concrete  arch  is  similar  to  that  used  for  a  masonry 
arch,  except  that  in  the  former  the  lagging  must  be  made 
smooth,  so  as  to  give  the  exact  shape  to  the  concrete  and  so 
constructed  that  the  concrete  will  not  adhere  to  it.  The  ad- 
hesion of  the  concrete  to  the  lagging  would  mar  the  smooth- 
ness of  the  finished  arch,  and  might  cause  difficulty  in  strik- 
ing the  centers.  This  last  item  is  of  more  serious  consequence 


Fig.    112.— Center    for    50-Ft.    Arch. 


Fig.  113.— Center  for  50-Ft.  Arch,  B.   &  O.  R.  R. 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


287 


than  a  possible  roughness  in  the  cases  where  the  bridge  is 
to  be  given  a  pebble-dash  or  other  rough  finish.  To  prevent 
the  concrete  from  adhering  and  to  obtain  a  smooth  surface, 
the  lagging  is  dressed  smooth  and  covered  with  cloth  or 
paper.  Soap  or  oil  are  used  to  diminish  the  tendency  to  ad- 
hesion. Where  centering  is  to  remain  in  place  for  a  long 
period,  however,  it  is  found  that  there  is  very  little  liability 
that  the  concrete  will  adhere  to  the  wood. 

As  in  masonry  construction,  arch  centers  for  concrete 
must  be  rigid  to  prevent  any  settlement  of  the  concrete. 
Since  timber  is  not  absolutely  rigid,  but  is  apt  to  settle, 
the  rise  of  the  centering  is  made  slightly  greater  than  the 
rise  designed  for  the  arch.  Mr.  Edwin  Thacher  provides 
for  an  additional  rise  in  the  centering  of  one  eight-hundredth 
of  the  span. 

Examples  of  Centering  for  Two  50-Ft.  Arches. — Two 
forms  of  centering  for  50-ft.  arches  are  shown  in  Figs.  112 
and  113,  the  latter  being  erected  without  support  between  the 
abutments. 

Centering  for  the  Pollasky  Bridge. — Fig.  114  shows  the 
centering  for  a  bridge  at  Pollasky,  Calif.  There  are  ten 
75-ft.  arch  spans.  Six  sets  of  false  work  were  used  for  the 
bridge,  and  were  moved  from  span  to  span  until  the  work 
was  completed.  Each  center  was  carried  on  five  bents  of 


Fig.   114.— Centering  and  Molds,   Pollasky  Bridge. 


288  REINFORCED    CONCRETE. 

8xl2-in.  posts  having  6xl2-in.  caps.  Just  below  the  caps  each 
longitudinal  line  of  posts  was  connected  by  a  pair  of  2x8-in. 
planks.  The  five  frames  of  the  center  were  supported  on  the 
caps  by  wedges.  The  ribs  of  the  center  on  which  the  2^x8- 
in.  lagging  was  placed,  were  pairs  of  2xl2-in.  plank  with  4x10- 
in.  fillers  between  them,  the  whole  nailed  together  by  7-in. 
spikes.  The  struts  consisted  of  a  pair  of  2x6-in.  planks  with 
a  4x6-in.  piece  between  them,  the  latter  projecting  up  into 
the  space  between  the  outside  planks  of  the  rib.  At  the  bot- 
tom each  strut  is  butted  on  a  6x8-in.  stringer.  On  either  side 
of  the  latter  was  a  1^2xl2-in.  plank,  and  ^-in.  bolts  passed 
through  the  plank  and  the  feet  of  the  struts.  In  laying  out 
the  centers  provision  was  made  for  a  1-in.  camber  by  using  a 
radius  of  61  ft.  11  in.  instead  of  62  ft.  3^4  in.  This  gives  a  rise 
of  10  ft.  ll$4  ins.  in  place  of  10  ft.  10^4  ins.  designed  for  the 
arch. 

Concreting  the  Arch. — Wherever  possible,  it  is  best  to 
make  the  concreting  of  the  arch  continuous,  so  that  there 
will  be  no  possibility  of  a  future  separation  on  a  plane  bound- 
ing two  days'  work.  Where  it  is  impracticable  to  concrete 
in  one  continuous  operation,  the  arch  ring  is  divided  into 
sections,  either  longitudinal  or  transverse,  each  section  repre- 
senting a  day's  work.  Both  methods  have  given  equally  satis- 
factory results.  In  either  case,  great  care  must  be  taken  at 
the  joining  of  the  new  concrete,  in  order  that  it  may  be  as 
nearly  monolithic  as  possible.  The  joint  is  made  rough,  to 
assist  in  securing  a  firmer  bond.  When  the  sections  are 
longitudinal,  they  are  so  chosen  that  none  of  the  reinforcing 
is  exposed  at  any  joint  between  two  days'  work.  When  the 
sections  are  transverse,  the  concreting  commences  either  at 
the  crown  or  the  springing,  care  being  taken  that  no  joint 
is  made  at  the  crown,  and  also  that  the  concreting  proceeds 
symmetrically  on  both  sides  of  the  crown.  The  sections  are 
not  bounded  by  vertical  planes,  as  in  the  case  of  longitudinal 
sections,  but  by  radial  planes,  so  that  all  pressure  brought 
upon  the  planes  of  juncture  will  be  normal  to  them.  Great 
care  must  be  taken  that  the  concrete  entirely  surrounds  the 
reinforcement,  and  that  the  reinforcing  material  is  not  dis- 
placed in  the  slightest  degree  in  concreting.  The  spacing 
and  location  of  reinforcing  material  are  designed  very  accu- 
rately to  meet  the  stresses  in  the  bridge,  and  unless  great 
care  is  taken  in  placing  the  reinforcement  and  in  concreting, 
the  reinforcement  will  not  fulfill  the  mission  for  which  it 
is  designed. 


BRIDGE  DESIGN  AND  CONSTRUCTION.  289 

Removal  of  Arch-Centering. — As  a  rule,  arch-centering 
should  be  left  in  place  as  long  as  possible.  Since  concrete 
shrinks  in  setting  and  since  wood  shrinks  in  drying,  there 
is  a  tendency  of  the  concrete  to  separate  from  the  centering 
unless  the  latter  be  kept  wet.  This  wetting  of  the  forms 
also  supplies  the  water  needed  by  concrete  in  setting.  There 
is  no  definite  rule  as  to  the  length  of  time  the  centering  re- 
mains in  place.  In  cases  where  the  arch  is  to  be  given  a 
form  of  tooled  finish,  so  that  the  forms  must  be  removed 
while  the  concrete  is  still  green,  or  in  cases  where  the  struc- 
ture is  in  several  spans  and  the  centering  is  needed  for  the 
others,  it  is  removed  earlier.  When  forms  are  removed 
early,  great  care  must  be  taken  that  they  are  lowered  grad- 
ually. While  concrete  begins  to  be  self-supporting  as  soon 
as  it  begins  to  set,  it  does  not  reach  its  maximum  strength 
for  some  time  after  setting,  so  that  the  removal  of  forms 
should  be  especially  provided  for.  The  devices  usually  em- 
ployed are  wedges  or  sand  boxes.  Wedges  can  be  driven 
out  gradually,  so  that  the  strain  comes  upon  the  arch  very 
slowly.  Sand  boxes  are  satisfactory  if  the  necessary  pre- 
cautions are  taken  to  keep  the  sand  from  packing  or  cak- 
ing, due  to  the  presence  of  dirt  or  cement.  Care  should  be 
taken  that  the  sand  is  very  clean,  and  that  the  boxes  are 
sealed  up,  to  prevent  the  entrance  of  foreign  matter. 

Grand  River  Bridge,  Grand  Rapids,  Mich. — As  a  typical 
example  of  bridge  construction,  the  following  description  of 
Grand  River  bridge  will  show  the  general  construction,  cen- 
tering and  details: 

There  are  five  arch  spans,  one  87  ft.,  two  83  ft.,  and 
two  79  ft.  One  of  the  79-ft.  spans  is  shown  in  Fig.  115. 
The  arch  rings  of  the  79-ft.  spans  are  18  ins.  thick  at  crown 
and  3  ft.  at  the  springing,  and  are  reinforced  by  two  courses 
of  \l/4-\r\.  Thacher  bars  placed  3  ins.  from  the  extradosal 
and  the  intradosal  faces. 

Each  pair  of  rods  is  connected  every  4  ft.  by  means  of  a 
£6-in.  rod  with  a  hook  at  each  end.  The  rods  have  3-in. 
washers  and  nuts  to  anchor  them  in  the  abutments,  and  are 


290 


REINFORCED    CONCRETE. 


made  continuous  from  end  to  end  of  span  by  means  of  turn 
buckles. 

The  arch  ring  was  built  in  transverse  sections,  each  sec- 
tion being  built  in  one  continuous  operation  in  a  day,  first 
the  crown  section,  then  the  two  skewback  sections,  and 
finally  the  intermediate  sections,  the  entire  ring  being  com- 
pleted in  five  days. 

Expansion  joints  in  the  spandrel  walls  were  formed  by 
laying  the  concrete  against  a  vertical  form  and  then  butting 
the  concrete  of  the  following  section  against  this  smooth 
surface  with  a  sheet  of  tar  paper  inserted  between.  Fig.  116 


Longitudinal       Section 

Fig.    115. — Details    of   79-Ft.    Span,    Grand    River   Bridge. 

is  instructive  in  illustrating  details  of  railing  and  forms  for 
making  them.     The  following  loads  were  assumed: 

Lbs.  per 

Dead  Load:  cu.  ft. 

Concrete     150 

Earth  filling 120 

Pavement,   12   ins.    deep 150 

Lbs.  per 

Live   Load:  sq.ft. 

Center  20-f t.  roadway ,...«..  250 

Remainder  of  roadway 150 

Sidewalks  100 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


291 


It  should  be  noticed  that  these  requirements  are  consid 
erably  above  the   actual  loads   that  will  usually   come  on  a 
bridge.      A  concentrated  load  was  assumed  on  the  roadway, 


,       Plan. 
Mold   for  "A 


Fig.   116.— Details   of  Railing  and   Forms,   Grand   River  Bridge. 

consisting  of  a  15-ton  steam  roller  having  axles  11-ft.  cen- 
ters with  6  tons  on  the  forward  wheel  4  ft.  wide  and  4^ 
tons  on  each  of  the  two  rear  wheels  20  ins.  wide  and  5  ft. 


292 


REINFORCED    CONCRETE. 


apart  on  centers.    The  ratio  — 

EC 

was  taken  as  20,  maximum 
compression  in  concrete  500 
Ibs.  per  sq.  in.  not  including 
temperature  stresses,  and  750 
Ibs.  per  sq.  in.  including  tem- 
perature stresses. 

Tension  and  shear  in  con- 
crete were  assumed  not  to 
exceed  75  Ibs.  per  sq.  in.  and 
reinforcement  stress  18,000 
Ibs.  per  sq.  in.  It  was  also 
required  that  the  percentage 
of  steel  reinforcement  in  the 
crown  should  be  at  least 
equal  to  2.  Centering  for  one 
of  the  83-ft.  spans  is  shown 
in  Fig.  117. 

The  Santa  Monica  Via- 
duct.—In  1902  a  viaduct  of 
two  67-ft.  spans  100  ft.  wide 
was  built  at  Santa  Monica, 
Cal.  by  Mr.  Carl  Leonardt, 
contractor,  Los  Angeles, 
Cal.,  according  to  plans  and 
specifications  prepared  by 
the  author.  Owing  to  the 
40-ton  trolley  cars,  the 
arches,  22  ft.  in  width,  were 
made  12^-in.  crown  and  16- 
in.  springing,  while  the  bal- 
ance of  the  viaduct  has  a 
thickness  of  only  6  inches  at 
the  crown  and  10  inches  at 
the  abutments.  The  rein- 
forcement consists  of  two 


i_ 


BRIDGE  DESIGN  AND  CONSTRUCTION. 


293 


nets  of  carrying  rods  spaced  6  inches  on  centers  for 
the  general  viaduct  and  3  inches  on  centers  under 
the  trolley  tracks.  The  distributing  rods  are  all  6  ins.  on 
centers  and  at  every  second  crossing  are  carefully  wired  to 
the  carrying  rods.  The  carrying  rods  in  the  lower  net  are 
y%  in.  in  diameter  for  one-third  of  the  arch  up  from  the 


60'0'Span- 


Fig.  118. — Centering  and  Reinforcement  for  Santa  Monica  Viaduct. 


abutments,  the  balance  of  the  rods  being  l/2  in.  in  diame- 
ter. The  top  net  consists  entirely  of  l/2-\n.  rods.  The  nets 
were  connected  by  means  of  No.  8  wires  tying  them  together 
and  keeping  them  apart.  The  intrado  net  was  clasped  in  hoop 
iron  chairs,  tacked  on  to  the  form  every  30  to  36  ins.  square, 


294  REINFORCED    CONCRETE. 

and  pulled  off  with  a  pair  of  pinchers  as  the  concreting  pro- 
ceeded. 

Owing  to  the  fact  that  the  Southern  Pacific  R.  R.  Co.'s 
tracks  run  under  the  north  span  on  a  curve,  the  clearance 
caused  the  necessity  of  a  slight  distortion  of  the  parabola, 
and  was  made  from  one  radius  65  ft.  and  two  radii  27  ft.  9  ins. 
The  total  rise  is  13  ft.  7  ins.  As  an  extra  precaution,  3  brack- 
ets or  counterforts  were  placed  under  the  trolley  line  part 
of  the  arch,  extending  from  skewbacks  over  one-third  of 
the  arch  towards  the  crown. 

For  arches  of  this  character  it  is  of  the  greatest  import- 
ance that  the  centering  is  carefully  designed,  placed  and 
adjusted  by  means  of  wedges  so  as  to  maintain  the  proper 
curvature  during  the  placing  of  reinforcement  and  concrete, 
and  that  any  shrinkage  or  swelling  of  the  lumber  is  com- 
pensated for.  The  forms  were  built  of  2xlO-in.  planks, 
spiked  together  and  braced  by  means  of  2xlO-in.  planks 
bolted  to  posts  and  joists.  The  posts  were  slotted  at  the 
lower  end  and  rested  on  2xl2-in.  planks  firmly  bedded  in  the 
ground,  being  made  adjustable  by  means  of  double  maple 
wedges.  The  lagging  consisted  of  Ix6-in.  boards  nailed  on 
top  of  the  rafters  transversely  across  the  viaduct,  and  on  top 
of  the  lagging  was  nailed  1x6  dressed  flooring  bent  exactly 
to  the  curve  of  the  arch.  After  both  arches  were  completely 
scaffolded  and  centered,  the  steel  rods  were  laid  from  the 
abutment  towards  the  center,  the  lower  netting  being  kept 
at  the  proper  distance  from  the  forms  by  means  of  hoop 
iron  snap  saddles,  so  arranged  that  they  could  be  withdrawn 
after  the  concreting  had  proceeded  sufficiently  to  insure  that 
the  steel  would  keep  its  position.  The  two  nets  were  kept 
at  the  proper  distance  by  No.  8  wire  stiffeners  at  every  eighth 
intersection. 

The  concreting  was  started  at  the  abutments  and  the 
work  made  continuous  until  finished.  The  mixture  was 
fairly  wet,  of  1  Portland  cement  to  4  parts  clean,  coarse, 
sharp  sand,  and  the  concrete  was  carefully  tamped  to  a 
thickness  regulated  by  straight  edges  with  prongs  penetrat- 


ABUTMENTS  AND  RETAINING  WALLS.          295 

ing  to  the  centering.  Three  weeks  after  the  concreting  was 
finished  the  backfilling  of  earth  and  sand  was  put  in  and 
the  roadway  completed. 

This  is  probably  the  lightest  Monier  viaduct  in  the  United 
States.  There  are,  however,  a  number  of  reinforced  con- 
crete bridges  in  Germany,  Switzerland  and  France  even  con- 
siderably lighter  in  construction.  Descriptions  of  these  can 
be  found  in  the  files  of  Beton  &  Eisen  and  in  catalogues  of 
Wayss  &  Freitag,  Hennebique  and  others. 


CHAPTER   IV. 
ABUTMENTS  AND  RETAINING  WALLS. 

Inasmuch  as  an  abutment  is  a  retaining  wall  with  a  sur- 
charge, we  will  consider  the  two  classes  of  construction 
tmdjer  one  head.  The  author  is  under  obligations  to  Prof. 
Milo  S'.'  Ketchum,  of  the  University  of  Colorado,  for  much  of 
the  following,  which  by  permission  has  been  compiled  from 
"The  Design  of  Walls,  Bins  and  Grain  Elevators." 

THEORIES  FOR  PRESSURE  OF  THE  FILLING. 

The  most  important  theories  for  finding  the  pressure  of  the 
filling  on  a  retaining  wall  are  as  follows: 

Rankine's  Theory. — Here  the  filling  is  assumed  to  con- 
sist of  an  incompressible,  homogeneous,  granular  mass,  with- 
out cohesion,  the  particles  being  held  in  position  by  friction 
on  each  other,  the  mass  being  of  indefinite  extent,  having  a 
plane  top  surface  and  resting  on  a  homogeneous  foundation, 
and  being  subjected  to  its  own  weight.  These  assumptions 
lead  to  the  ellipse  of  stress  and  make  the  resultant  pressure 
on  a  vertical  wall  parallel  to  the  top  surface.  The  pressure 
on  other  than  vortical  walls  can  be  determined  by  the  el- 
lipse of  stress. 

Weyrauch's  Theory. — Here  the  filling  is  assumed  to  be 
without  cohesion  and  to  be  held  in  equilibrium  by  friction 
of  the  particles  on  each  other.  It  is  also  assumed  that  the 
forces  upon  any  imaginary  plane  section  through  the  mass 
of  earth  have  the  same  direction.  These  assumptions  lead 
to  two  formulas,  one  giving  the  amount  of  the  thrust  and 
the  other  giving  its  direction,  the  angle  that  the  resultant 
makes  with  a  normal  to  the  wall.  The  formulas  deduced 
by  Weyrauch  may  be  obtained  more  simply  by  means  of  the 
ellipse  of  stress,  and  are  therefore  subject  to  the  same  lim- 
itations. 

296 


BRIDGE  DESIGN  AND  CONSTRUCTION.  297 

Coulomb's  Theory.  —  Here  a  wedge  is  assumed,  having 
the  wall  as  one  side  and  a  plane  of  rupture  as  the  other  side, 
which  exerts  a  maximum  thrust  on  the  wall.  The  plane  of 
rupture  lies  between  the  angle  of  repose  of  the  rilling  and 
the  back  of  the  wall.  It  may  coincide  with  the  plane  of 
repose.  For  a  wall  without  surcharge  (horizontal  surface 
back  of  the  wall)  and  a  vertical  wall,  the  plane  of  rupture 
bisects  the  angle  between  the  plane  of  repose  and  the  back 
of  the  wall.  This  theory  does  not  determine  the  direction 
of  the  thrust,  and  leads  to  many  other  theories  having  as- 
sumed directions  for  the  resultant  pressure. 

Cain's  Theory.  —  Prof.  William  Cain  assumes  that  the 
resultant  thrust  makes  an  angle  with  the  normal  equal  to 
0',  the  angle  of  friction  of  the  filling  on  the  back  of  the  wall, 
or  equal  to  0,  the  angle  of  repose  of  the  filling,  if  0'  is  greater 
than  0. 

Other  authorities  assume  that  the  resultant  thrust  is  nor- 
mal to  the  back  of  the  wall.  For  a  smooth  vertical  wall 
without  surcharge,  all  of  the  above  formulas  lead  to  the 
same  result  for  the  amount,  direction  and  point  of  applica- 
tion of  the  resultant  thrust. 

Trautwine's  Theory.  —  In  Trautwine's  Engineers'  Pocket- 
book  it  is  assumed,  for  a  wall  nearly  vertical,  that  the  plane 
of  rupture  in  all  cases  bisects  the  angle  between  the  plane 
of  repose  and  the  back  of  the  wall.  This  theory  gives  cor- 
rect results  for  a  vertical  wall  with  horizontal  surface  back 
of  the  wall,  but  is  in  error  for  all  other  cases. 

Rankine's  Formulas.  —  For  vertical  retaining  walls  with- 
out surcharge: 


q  =  wy 


298  REINFORCED    CONCRETE. 

where 

P  =  resultant  earth  pressure  per  foot  length  of  wall. 
w  =  weight  of  filling  per  cubic  foot. 
y  =  depth  of  foundation  below  earth  surface. 
q  —  horizontal  pressure  at  a  depth  equal  to  y. 
h  =  vertical  height  of  wall  in  feet. 
0  =  angle  of  repose  of  the  filling. 
For  angle  of  surcharge  =  8,  Rankine's  formula  is: 
cos  5  —  V  cos2  8  —  cos2  0 


Cain's  Formulas.-  If  <})'  —  angle  of  friction  of  the  filling  on 

the  back  of  the  wall 
0  =  angle   between   back    of   wall    and 
the  horizontal   running  back   into 
the  filling 

for  8  =  0 


^-^7 (44) 

•  si"    ( (b  -4-  0">    sin  0 
where  n  —  -\  l~ 


\ 

If    0'  =  0,  we  have 

p  =  %whz  tan2  U5°  —  -TJ- j (45) 

For  surcharge  =  8  ,  the  value  of  P  is  the  same  as  in  For- 
mula (45)  except  that 

I  sin   (0  +  0')  sin  (0  —  8) 
^|  cos  0'    cos  8 

For  inclined  wall  with  horizontal  surfaces : 
sin  (  e  -J- 


sin    # 


)',in^+*)--(46> 


,'sin   (0  +  0')   sin0 
W=AL:n^/  _j_e)    sin    0 

For  inclined  wall  with  surcharge  =  cJ ,  the  value  of  P  is  the 
same  as  in  Formula  (46)  except  that 


/sin  (0  +  07)   sin  (0  —  8) 
n  ^^sin  (0'  +  0  )  sin  (0—5) 


ABUTMENTS  AND  RETAINING  WALLS.          299 

GENERAL    DISCUSSSION. 

Thrust. — In  calculating  the  thrust  on  a  retaining  wall, 
great  care  must  be  used  in  selecting  the  proper  value  for 
the  angle  of  repose  and  the  conditions  of  surcharge,  as  the 
value  of  the  thrust  increases  very  rapidly  as  the  angle  of 
repose  decreases  and  as  the  angle  of  surcharge  increases. 

Back  Filling. — The  filling  back  of  the  wall  should  be  de- 
posited and  tamped  in  approximately  horizontal  layers,  or 
in  layers  sloping  back  from  the  wall,  and  a  layer  of  sand, 
gravel  or  other  porous  material  should  be  deposited  between 
the  fill  and  the  wall  to  drain  the  fill  downwards. 

Drainage. — To  insure  drainage  of  the  filling,  drains  should 
be  provided  back  of  the  footing,  and  weep-holes  located  in 
the  body  of  the  wall  at  close  intervals.  The  filling  in  front 
of  the  wall  should  also  be  carefully  drained. 

Expansion  Joints. — In  order  to  prevent  the  heaving  of 
the  foundation  by  frost,  it  is  usual  to  provide  from  2l/2  to  5 
ft.  of  filling  in  front  of  the  wall.  While  in  solid  masonry 
walls  it  is  necessary  to  locate  expansion  joints  at  intervals 
of  from  30  to  50  ft.,  to  prevent  cracks,  such  joints  are  fre- 
quently omitted  in  retaining  walls  of  reinforced  concrete, 
and  reinforcement  is  placed  in  the  direction  of  the  length  of 
the  wall  for  such  purpose. 

Temperature  Cracks. — Mr.  A.  L.  Johnson  gives  the  fol- 
lowing formula  for  the  amount  of  reinforcement  required  to 
prevent  temperature  cracks.* 

tensile  strength  of  concrete 
Area  of  steel  =    ~ el^tic"limif^f^te~el~    X  area  of  concrete. 

For  mild  steel  the  elastic  limit  is  33,000  Ibs.  per  sq.  in., 
the  tensile  strength  of  concrete  is  about  200  Ibs.  per  sq. 

in.,   and  the   area  of    steel  is  1-^v  of    the    area    of    the    wall. 

165 

For  high  steel  of  an  elastic  limit  of  55,000  Ibs.  per  sq.  in., 
we   find   the   area   of   steel   required   to   prevent  temperature 


*Railroad  Gazette,  March  13,  1903. 


300 


REINFORCED   CONCRETE. 


cracks  equal  to  —  of  the  area  of  the  wall. 

£7o 
Mr.  W.  W.  Colpitts  recommends  0.6  sq.  in.  of  steel  per  sq.  ft. 

of  concrete*  which  is  —  the  area  of  the  wall. 

^T-V 

The  author  recommends  a  wire  fabric  of  high  carbon  steel 
with  the  carrying  rods  running  horizontally  and  located  not 
more  than  2  ins.  from  the  face  of  the  wall. 


/:     / 

/  i  i     UiC'M'idd/e  Third 
/     I'dJItQm    i 

''     k,^il__!:iln""'""  Center  of  Base 
/''          BA*^B^ 


Fig.   119. — Diagram  of  Forces   for  Masonry  Retaining  Wall. 

MASONRY  RETAINING  WALL. 

Design  a  retaining  wall  by  means  of  the  ellipse  of  stress, 
where  height  =  h,  angle  of  surcharge  =22°  30',  and  the  angle  of 
repose,  37°  30*.  See  Fig.  119. 


•Railway  Age,   January,    1904. 


ABUTMENTS  AND  RETAINING  WALLS.          301 

Calculation  of  Resultant  Pressure. — To  calculate  the  re- 
sultant pressure,  P,  proceed  as  follows:  Draw  AO  parallel  to  the 
surcharge  A'M"  and  at  any  convenient  point  O  in  AO  draw  OD 
at  right  angles  to  AO.  Draw  OM  vertical  and  locate  M  by  strik- 
ing the  arc  DM  with  O  as  a  center,  and  OD  as  a  radius.  Draw 
OC,  making  the  angle  0  with  OD.  At  any  point  e  in  OD  describe 
an  arc  tangent  to  OC  and  cutting  OM  at  /.  Through  M  draw 
MG  parallel  to  ef.  Bisect  the  angle  DGM  and  through  O  draw 
OR  parallel  to  GR'.  Then  OR  is  the  principal  axis  of  the  el- 
lipse of  stress  and  OM"  the  maximum  stress  that  can  occur  in 
the  filling.  To  calculate  the  maximum  stress  at  A,  draw  OG' 
at  right  angles  to  the  back  of  the  wall  AA',  and  make  OG'  =  OG. 
With  G'  as  center  and  OG'  as  radius,  describe  an  arc  cutting  the 
principal  axis  OR  at  t.  Draw  G't,  and  with  G'  as  a  center  and 
GM  as  a  radius  locate  M'.  Then  M'O  acting  as  shown  is  the  in- 
tensity of  the  stress  at  A.  The  resultant  pressure  P  is  equal  to 
the  area  of  the  stress  triangle  AA'N  X  w,  where  w  is  the  weight 
per  cu.  ft.  of  the  fill.  P  acts  on  AA'  at  Vz  the  height  of  the  wall. 

The  weight  of  the  masonry,  W,  combined  with  P  gives  the 
resultant  E,  which  must  cut  the  foundation  within  the  middle 
third.  The  vertical  component  of  E  is  F. 

Stability  Against  Overturning.— Through  B  draw  O'S  and 
produce  cd  to  S.  Then  the  factor  of  safety  against  overturning 

is  £;  .     HE  passes  through  B,  the  wall  would  be  on  the  point  of 
overturning  and  -7—  would  be  equal  to  1. 

Stability  Against  Sliding. — The  angle  of  friction  of  the 
masonry  against  the  footing  we  will  take  as, 

<£'  =  30° 

Through  O'  draw  gk,  cutting  the  base  of  the  wall  at  i  at  30° 
to  the  vertical.  Then  the  factor  of  safety  against  sliding 
will  be 


302  REINFORCED    CONCRETE. 

Stability  Against  Crushing.  —  The   direct  pressure  per  sq. 
ft.  will  be 

F 


where  BA  is  the  width  of  the  base. 

l/dcf/e  Third 


Fig.  120.  —  Diagram  of  Moments  for  Masonry  Retaining  Wall. 

The   pressure    due   to   the   bending   moment    will   be    (see 
Fig.    120): 

6F6* 


The  maximum  pressure  will  be 

p  =  pi+p*t 
and  the  minimum, 

p  —  pi  —  h. 

If,  in  addition  to  the  foregoing  assumptions,  we  assume 
the  wa)l  to  be  18  ft.  high, 

A'B'  =  2  ft  Gins. 
AB  =  7  ft.  6  ins., 

the  batter  of  the  back  wall  AA'  %  in.  per  ft.,  the  masonry 
to  weigh  150  Ibs.  per  cu.  ft,  and  the  fill,  w,  100  Ibe.  per  cu.  ft., 
we  find  the  following  result: 

*  Note.—*  is  distance  from  center  of  base  to  where  resultant  E  cuts  base. 


ABUTMENTS  AND  RETAINING  WALLS.  303 

P   -  ^ |-^  X  100  =  4880. 

2.5  +  7.5 
W  = £ x  18  x  15°  =  1350°  lbs-  Per  lin-  ft-  of  wall. 

E  =  16500 
6  =1.1  ft. 
F  =  16000 
16000 
fr 


P2 
P 


7.5 

6F6 


=  2133 
6  X  16000  x   1.1 


±1877,  where  d=J5A 


d2  7.5  X  7.5 

4010  or  256. 

REINFORCED    CONCRETE    RETAINING    WALL    OF 
BEAM   TYPE. 

Design  a  reinforced  concrete  retaining  wall  of  the  beam 
type,  to  carry  a  sand  filling  16  ft.  high,  weighing  100  lbs.  per 
cu.  ft.,  and  having  an  angle  of  repose  of  35°,  and  sloping 
back  at  that  angle. 


Fig.    121. — Diagram    of    Forces    for    Reinforced    Concrete    Retaining 

Wall. 

The  Vertical  Beam. — The  bottom  of  the  foundation  will 
need  to  be  about  4  ft.  deep  and  we  will  assume  the  stem  of 
the  wall  to  be  18  ft.  high.      In  Fig.  121  the  pressure  is 
P  •-=  A  SEN  x  w  =  12,200  Ibs. 


304  REINFORCED    CONCRETE. 

and  is  parallel  to  the  top  surface.      The  horizontal  compo- 
nent of  P  is 

H=  10,000  Ibs. 

The  bending  moment  about  B  is 

M'  =  10,000  X  6  =  60,000  ft.  Ibs.,  for  1  ft.  wide,  or  inch  Ibs. 
for  1  in.  wide. 

Instead  of  using  Table  XLVI,  we  will  make  w  =  12,  />  =  0.006 
and  /"  =  16,000.      According  to  Table  XXXIX,  we  have, 

k 
1  — -  TT  =  0.896  and 


60,000 

=  26.6  ms. 


1.006  X  16,000  X  0.896 
and  h  =  30  ins.     The  top  is  12  ins.  thick. 

The  steel  reinforcement  required  per  foot  width  of  the 
wall  is 

A*  =  26.6  X  12  X  0.006=1.915  sq.  ins. 
Three  1-in.  rods  =  3  X  0.7854  =  2.356  sq.  ins, 
or  1-in.  rods,  4  ins.  on  centers,  with  4  in.  by  6-in.  mesh  No.  7 
and  No.  11  fabric  on  both  sides  for  temperature  stresses. 

Foundation. — We  will  assume  that  the  footing  is  10  ft. 
long,  as  shown  in  Fig.  122.  Then  the  pressure  on  the  plane 
A'F  is 

P'  =  19,900  Ibs. 
The  weight  of  the  earth  prism  AA'BF  is  7,425  Ibs.  and 

p  =  25,000  Ibs. 

Combining  P  and  the  weight  of  the  wall,  which,  including  re- 
inforcement, we  will  call  7,725  Ibs.,  we  have 

£  =  31,000  Ibs., 

which  cuts  the  base  2  ft.  to  the  left  of  the  center,  outside 
the  middle  third. 


ABUTMENTS  AND  RETAINING  WALLS.          305 


Now 


F  =  24,000  Ibs.,  and 

/>i  =  2,400  Ibs.  per  sq.  ft., 

6F6 
p2  =  — p-  =  ±2,880  Ibs.,  hence  (d= 

=  5,280  or  -480  Ibs.  per  sq.  ft. 


Fig.    122. — Diagram    of   Forces    for   Reinforced    Concrete    Retaining 

Wall. 


306 


REINFORCED    CONCRETE. 


Since  the  foundation  cannot  take  tension,  we  wil!  hav* 
to  let  all  the  load  be  taken  by  compression  as  follows: 

2F       2  X  24000 
p'  =  -^  =       3  x  3     •  =  5,330  Ibs.  per  sq.  ft. 

This  pressure  is  safe  for  good  gravel  or  clay.  While  the 
resultant  cuts  outside  the  middle  third,  the  base  is  sufficiently 
long  for  the  conditions  named. 

To  calculate  the  bending  moment  to  the  left  of  D,  take  the 
lower  stress  diagram,  4-5-6-7,  Fig.  122,  and  multiply  it  by  the 
distance  of  its  center  of  gravity  to  the  left  of  D. 


Then  M'  = 


Table  XLVI  gives  for  a  moment  of  49,465, 

h  =  24. 
and  for  40,880, 

7z  =  22. 

We  will  put  in  0.17  X  4^  = 
0.765  sq.  ins.,  or  1-in.  rods  4^ 
ins.  on  centers,  the  full  length 
of  the  foundation.  Rods  will  be 
placed  2  ins.  from  top  of  the  in- 
ner surface,  as  shown,  and  these 
rods  we  will  make  1  in.  in  di- 
ameter, and  8  ins.  on  centers. 
See  Fig.  123. 


REINFORCED      CONCRETE 

RETAINING  WALL  WITH 

COUNTERFORTS. 

Design  a  reinforced  concrete 
retaining  wall  with  counterforts 
to  carry  a  sand  filling  175^ 
ft.  above  ground,  which 


?ods,  6  "c.  toe. 


Fig.    123.— Section    of   Rein- 
forced   Concrete    Retain- 
ing Wall. 


weighs  100  Ibs.  per  cu.  ft.,  has  an  angle  of  repose  of  37°  30', 
and  carries  a  railroad  track  which  is  equivalent  to  a  sur- 
charge of  6  ft.  Counterforts  to  be  spaced  10  ft.  on  cen- 
ters, as  shown  in  Fig.  125. 


ABUTMENTS  AND  RETAINING  WALLS. 


307 


Calculation  of  Pressure  P. — The  pressure  P'  on  the  vertical 
plane  2-B  is  calculated  graphically  as  shown  in  Fig.  124. 

A  SeN  X  w  =  pressure-  on  the  vertical  plane  B-Q,  and  the 
pressure  triangle  is  5-6-4.  Resultant  pressure  P'  acts  through 
the  center  of  gravity  and  is  equal  to  the  area  5-2-3-4,  equals  9,200 
Ibs.  Resultant  pressure  P"  acting  on  plane  G-2  is  found  to  be 
7,720  Ibs. 


Fig.    124.— Moment    and    Stress    Diagram    for   Reinforced    Concrete 
Retaining  Wall. 

The  weight  of  the  prism  of  filling  O-1-2-G  is  15,000  Ibs.,  and 
combining  this  weight  with  P',  we  have 
p  =  17,500  Ibs. 

acting  as  shown.  The  weight  of  the  concrete  wall  per  linear 
foot  is  approximately  6,500  Ibs.,  which  when  combined  with 
P  gives 

E  =  23,200  Ibs. 


308 


REINFORCED   CONCRETE. 


Resultant  E  cuts  the  base  at  a  distance  1.6  ft.  from  the  center, 
and  the  vertical  component  of  E  is 

F  =  21,500  Ib's. 

Vertical    Wall. — In    designing    the    center    slab    the    span 
will  be  taken  as  10  ft.      (Where  the  wall  has  no  cracks  the 


r 


i 6 1«- Ground  level 


Fig.    125. — Plan   and   Section   of  Wall,   Showing  Reinforcement. 

actual  span  is  less  than  the  clear  span  of  8  ft.  6  ins.)  Tak- 
ing the  bottom  strip,  1  ft.  wide,  and  10  ft.  long,  we  design 
a  simple  beam  that  will  carry  a  load  of  623  Ibs.  per  linear  ft. 


ABUTMENTS  AND  RETAINING  WALLS.          309 


623  x  102 
M  =  •  -  --  =  7,788  ft.  Ibs.  (or  inch  Ibs.  per  inch). 


Again  making  n  —  12,  p  =  0.006,  and  /  =  16,000,  we  get 


7  788 
d  =\/n  n^g  ..  -la  nnn  v,  n  ona  =  9.5  ins.  and  h  =  12  ins. 


~\  0.006  X  16,000  X  0.896 
The  steel  area  per  foot  is : 

0.006  X  9.5  X  12  =  0.684  sq.  ins., 

or  24-in.  rods,  8  ins.  on  centers,  grading  the  distance  between 
rods  according  to  the  decreasing  pressure  toward  the  top. 
See  Fig.  125.  The  temperature  stresses  will  be  taken  care 
of  by  means  of  4  X  6  ins.  No.  7  and  No.  11  fabric,  to  which 
the  rods  are  fastened  by  wire — usually  doubled  No.  18  an- 
nealed wire. 

Counterforts.— The  bending  moment  on  a  counterfort  at  OG 
in  Fig.   124  will  be, 

jlf'  =  7,720X8X10  =  617,600  ft.   Ibs,   or  7,411,200  in.   Ibs. 
If  the  counterfort  is  18  ins.  wide  we  have: 


M  =    '    tg        =  411,733  in.  Ibs.,  for  1  in.  width. 


7,411.200 
18 

By  Formula  (11) 


and  for  /  =  16,000,  p  =  0.006,  and  n  =  15,  we  find 
(l-|)  =  0.885. 


411  733 
Hence  d=+L  nnft       ,R  nnn^v  n  «Q^  =  70  ins.  =  5  ft.  10  ins. 

%|U.UUO   A    lOivUU   /\   U.ooO 

Steel  area  for  18  ins.  width  is 

0.006  X  70  X  18  =  7.56  sq.  ins., 

or  8  rods,  1%  ins.  diameter.  Rods  */2  in.  in  diameter  will 
be  placed  as  shown  in  addition  to  fabric  to  take  vertical  and 
horizontal  shear. 


310  REINFORCED    CONCRETE. 

Foundation.  —  In  Fig.  124  the  direct  pressure  pi  is  1,600  Ibs. 
per  sq.  ft.,  while  the  pressure  due  to  the  moment  is 


p2  =.-  -^—  =  +1,120  Ibs.  per  sq.  ft. 

Then 

/>  =  2,720  or  480  Ibs.  per  sq.  ft. 

which  is  entirely  safe  for  ordinary  conditions.  The  maximum 
moment  at  K  in  the  outer  toe  is  found  in  Fig.  124  by  taking  the 
moment  area  to  the  left  of  K,  and  is 

M<  =  (2'72°  +2  2'0°°)  5  X  2.6  =  30,680  ft.  Ibs. 

By  Table  XLVI  this  corresponds  to  a  slab  between  19  and 
20  ins.  However,  we  have  assumed  24  ins.  We  will  use 
steel  area  of  0.15  sq.  in.  per  inch,  or  %-in.  rods  4  ins.  on 
centers  and  place  %-in.  rods  8  ins.  on  centers  at  top  of  slab 
as  shown.  At  the  bottom  we  will,  in  addition  to  4  X  6-in. 
fabric  of  Nos.  7  and  11  gage,  place  fys-in.  distributing  rods 
longitudinally  8  ins.  on  centers. 

Conclusion.  —  It  will  be  noticed  that  in  the  foregoing  ex- 
ample a  rib  is  placed  longitudinally  underneath  the  heel  and 
the  toe  of  the  base.  This  is  largely  for  the  purpose  of  con- 
fining the  soil  between  the  two  ribs  and  to  aid  in  preventing 
sliding. 

For  long  retaining  walls  the  face  slab  should  be  decreased 
in  thickness  from  bottom  towards  the  top,  as  the  saving  in 
concrete  will  be  greater  than  the  additional  cost  of  the  ta- 
pered forms. 

RETAINING  WALL  FORMS. 

Setting  the  Forms.  —  In  setting  the  forms,  great  care  is 
taken  to  set  the  apparatus  on  a  firm  base  and  thoroughly 
brace  it.  The  first  panels  are  set  in  a  line  end  to  end  with 
tight  joints  and  absolutely  leveled.  After  the  lower  line  is 
set  correctly,  the  others  will  come  all  right,  and  as  soon  as 
the  lower  line  is  in  place  the  concreting  may  begin.  The 
concrete  is  placed  in  layers  not  to  exceed  12  ins.  in  thick- 
ness and  the  face  is  thoroughly  spaded  so  as  to  bring  the 


ABUTMENTS  AND  RETAINING  WALLS. 


311 


The  following  tables  give  the  intensity  of  the  horizontal 
pressure,  p,  at  any  depth,  h,  the  total  pressure  H,  above  the 
section  considered  and  the  overturning  moment,  M,  in  inch 
Ibs.,  at  the  section  A-B -.—("Designing  Methods") 


HORIZONTAL  SURFACE 

SURCHARGE.  0=30° 

a/=1001bs. 

a/=100lbs. 

E 

1  —  f* 

^ 

1 

f  \o'^vm  : 

tf 

33  * 

-XA\0'J*  ''f 

•/£&    a 

r 

iS 

^  — 

d 

•^—  — 

— 

p 

TABLE  LXIV-A 

TABLE  LXIV-B 

,  _ 

H=P 

i   a 

Overturning 
Moment 

Pcos0 

4  / 

H=P 

Overturning 
Moment 

h 

1    ^    7/J/f 

=  1-0 

h 

•74. 

cos 

o  7% 

A/fsec  V 

l-O  Zf  fl 

wh? 

a/A3X12 

wh 

wh? 

a/A3  X  12 

Feet. 

Pounds. 

Pounds. 

Inch  Pounds. 

Feet. 

Pounds 

Pounds. 

Inch  Pounds. 

j 

33 

17 

67 

1 

75 

38 

150 

2 

67 

67 

533 

2 

150 

150 

1200 

3 

100 

150 

1800 

3 

225 

338 

4050 

4 

133 

267 

4267 

4 

500 

600 

9600 

5 

167 

417 

8333 

5 

375 

938 

18750 

6 

200 

600 

14400 

6 

450 

1350 

32400 

7 

233 

817 

22867 

7 

525 

] 

838 

51450 

8 

267 

1067 

34133 

8 

300 

2 

400 

76800 

9 

300 

1350 

48600 

9 

675 

3038 

109350 

10 

333 

1667 

66667 

10 

rso 

3 

750 

150000 

11 

367 

2017 

88733 

11 

825 

4538 

199650 

12 

400 

2400 

115200 

12 

XX) 

5 

400 

259200 

13 

433 

2817 

146467 

13 

975 

6338 

329550 

14 

467 

3267 

182933 

14 

1 

)50 

7 

350 

411600 

15 

500 

3750 

225000 

15 

1125 

8438 

506250 

16 

533 

4267 

273067 

16 

11 

JOO 

8 

600 

614400 

17 

567 

4817 

327533 

17 

1275 

10838 

736950 

18 

600 

5400 

388800 

18 

13 

550 

12 

150 

874800 

19 

633 

6017 

457267 

19 

1425 

13538 

1028850 

20 

667 

6667 

533333 

20 

u 

>00 

15 

000 

1200000 

21 

700 

7350 

617400 

21 

1, 

>75 

16 

538 

1389150 

22 

733 

8067 

709867 

22 

1650 

18150 

1597200 

23 

767 

8817 

811133 

23 

r 

r25 

19 

838 

1825050 

24 

800 

9600 

921600 

24 

1800 

21600 

2073600 

25 

833 

10417 

1041667 

25 

1* 

575 

23 

438 

2343750 

26 

867 

11267 

1171733 

26 

1950 

25350 

2636400 

27 

900 

12150 

1312200 

27 

2( 

)25 

27 

338 

2952450 

28 

933 

13067 

1463467 

28 

2100 

29400 

3292800 

29 

967 

14017 

1625933 

29 

2] 

75 

31 

538 

3658350 

30 

1000 

15000 

1800000 

30 

2250 

33750 

4050000 

312 


REINFORCED    CONCRETE. 


fine  mortar  to  the  face,  or  a  cement  mortar  of  same  mixture 
as  mortar  in  the  concrete  may  be  slushed  along  the  face. 

The  next  panel  above  may  be  placed  as  the  concrete  is 
brought  up  without  interfering  with  the  placing  of  the  con- 
crete so  that  carpenters  and  concrete  men  may  be  working 
at  the  same  time  and  place. 

Removing  the  Forms. — After  the  concrete  against  the 
lower  line  of  panels  is  placed  the  panels  can  be  removed 
after  18  hours  in  the  summer  and  24  to  30  hours  in  the  win- 
ter, and  floating  of  the  surface  can  be  started,  even  though 
concreting  may  be  going  on  at  the  top  of  the  wall.  After 
the  proper  lapse  of  time  on  the  other  lines  of  panels  they 
may  be  removed  and  the  wall  floated  until  the  top  is  reached. 
To  remove  the  panels,  the  wedges  are  drawn,  the  blocks  are 
removed,  and  the  panels  are  drawn  out  endwise. 

When  forms  are  removed  the  walls  should  be  green  and 
easily  worked.  The  floating  is  done  with  wooden  floats  or 
cement  bricks.  Cement  plaster  should  be  positively  forbid- 
den, though  fresh  water  may  be  splashed  over  the  wall 
to  assist  the  rubbing  off  of  all  board  marks  or  ridges  and 
to  bring  to  a  uniform  smooth  surface. 

Expansion  Joints. — Expansion  joints  are  formed  from  25 
to  35  ft.  apart  by  placing  tar  paper  through  the  entire  area 
of  wall  section.  The  number  of  thicknesses  depends  upon 
the  season  of  year,  only  1  in  the  summer  and  5  or  6  in  the 
winter. 

The  first  cost  of  these  forms 
is  high,  but  for  a  considerable 
stretch  of  work  they  can  be 
used  over  and  over  again  if 
made  of  good  material  and  tak- 
en care  of  properly. 

Wall  Form  Tie.— Fig.  127  is 
a  simple  form  for  a  heavy  wall, 
such  as  is  employed  by  the  au- 
thor. The  tie  is  formed  of  wire, 
which  is  tightened  by  twisting,  as  shown. 


Fig.   127.— Wall  Form   Tie. 


ABUTMENTS  AND  RETAINING  WALLS. 


313 


EXAMPLES  OF  CONSTRUCTION. 
Retaining  Wall,  Paris,  France. — Fig.  128  shows  a  modifi- 
cation of  the  usual  type  of  wall  with  counterforts.  This  wall 
is  of  Hennebique  construction  and  was  built  to  support  the 
sides  of  a  depressed  street  near  the  gardens  of  the  Troca- 
dero,  at  the  Paris  Exposition  of  1900.  The  wall  was  built 


Horizontal     Section   A-B. 


128.  —  Retaining   Wall    for    Sunken    Street,    Paris,    France. 


in  sections  about  20  ft.  in  length,  each  section  being  made 
up  of  a  facing  strengthened  at  its  back  by  three  buttresses. 
Two  horizontal  beams  connected  the  facing  and  the  but- 
tresses. The  base  slab  was  strengthened  at  the  toe  of  the 
wall  by  buttresses  underneath  the  street  level,  as  shown. 


314  REINFORCED    CONCRETE. 

By  this  arrangement  of  horizontal  beams  the  retaining 
wall  is  assisted  in  sustaining  the  earth  pressure  by  the 
weight  of  this  earth  upon  the  horizontal  beams — and  does 
not,  as  in  ordinary  retaining  walls,  depend  upon  its  weight 
alone. 

The  employment  of  the  two  separate  beams  at  different 
levels,  instead  of  the  one  at  the  same  total  width,  results  in 
largely  decreasing  the  thrust  of  the  earth  upon  the  vertical 
face— and  reduces  the  excavation  required.  The  two  rear 
beams  are  only  used  in  nine  panels,  as  the  retaining  wall  is 
protecting  a  sloped  street,  and  the  height  of  the  wall  is 
reduced  at  one  end  so  as  to  need  but  one  base.  The  width 
of  the  front  horizontal  beam  was  fixed  by  assuming  a  top 
load  of  2,048  Ibs.  per  sq.  ft.  upon  soil  of  this  nature.  The 
width  of  the  back  of  the  wall  was  figured  with  an  average 
factor  of  safety  of  2,  in  calculating  the  moment  of  stability 
of  the  wall. 

The  reinforcement  of  the  vertical  face  consists  of  two 
series  of  vertical  bars  combined  with  one  series  of  horizontal 
bars,  the  distances  between  which  increase  towards  the  top 
of  the  wall.  These  bars  are  bent  over  at  right  angles  at 
the  top  to  give  support  for  a  coping  of  the  same  construc- 
tion as  the  facing.  The  illustration  gives  the  sizes  of  the 
different  bars  or  rods. 

t  Retaining  Wall,  Great  Northern  Ry.,  Wash. — A  good  ex- 
ample of  a  high  reinforced  concrete  retaining  wall  is  here 
reprinted.*  The  wall,  Fig.  129,  is  of  the  counterfort 
type  and  is  used  in  the  terminal  yard  of  the  Great  Northern 
Railway  at  Seattle,  Wash.  The  wall  supports  a  street  and 
varies  in  height  from  2  to  37.8  ft.  and  is  approximately  2,000 
ft.  in  length.  Mr.  C.  F.  Graff  of  the  engineering  staff  of 
the  Great  Northern  Railway  states  that  a  comparison  of 
cost  between  a  plain  concrete  wall  of  gravity  section  and 
a  wall  of  counterfort  type  gave  a  noticeable  saving  for  the  lat- 
ter, as  shown  in  Table  LXIV.  The  heights  vary  from  10  to 

*Reid's  Concrete  and  Reinforced  Concrete  Construction. 


ABUTMENTS  AND  RETAINING  WALLS. 


315 


40  ft,  the  section  of  wall  is  assumed  1  ft.  long,  figuring  the 
amount  of  steel  used  at  4*/2  cts.  per  lb.,  evaluated  in  terms 
of  concrete  at  $6.00  per  cu.  yd.  in  place. 


Part-     Plan., 
Fig.    129.— Retaining    Wall,    Great    Northern    Ry.,    Seattle,    Wash. 

TABLE  LX IV.— COMPARATIVE  QUANTITIES  OP  CONCRETE  IN  PLAIN  AND 
REINFORCED  CONCRETE  RETAINING  WALLS. 


Height  Wall 
in  feet. 

Cu.  Ft.  Concrete 
Plain  Wall. 

Cu.  Ft.  Concrete 
Reinforced  Wall. 

Saving 
Per  cent. 

10 
20 
30 
40 

44 
110 
226 
396.4 

34.9 
69.9 
127.8 

20.4 
36.4 
43.4 
45.0 

316  REINFORCED    CONCRETE. 

It  was  assumed  in  this  estimate  that  the  extra  cost  for 
forms  and  a  higher  grade  of  concrete  for  a  reinforced  wall 
was  counterbalanced  by  the  saving  in  piling  necessary  for 
the  plain  concrete  wall.  Fig.  129  shows  elevation,  section 
and  plan  of  wall  at  its  highest  point;  where  it  joins  the  portal 
at  the  highest  point  it  is  37  ft.  7  ins.  high.  The  gen- 
eral dimensions  and  reinforcement  employed  are  shown  on 
the  drawing.  In  computing  sections  of  face  and  base  of  wall 
they  were  considered  as  composed  of  a  series  of  independent 
beams  lying  side  by  side,  giving  an  additional  factor  of 
safety,  as  there  is  really  a  supported  slab  action.  Piles  were 
driven,  as  shown,  to  compact  the  earth,  to  support  the  toe 
of  the  wall  and  to  prevent  the  structure  from  sliding  for- 
ward. Scaffolding  was  put  up  to  facilitate  the  erection  of 
the  skeleton  steel  work.  Near  the  top  of  this  scaffolding 
the  two  top  1-in.  horizontal  face  bars  were  securely  fastened 
in  exact  line  and  elevation  and  the  long  diagonal  1^4 -in. 
bars  running  down  the  back  of  each  rib  were  hooked  on  these 
and  swung  into  proper  position  at  the  bottom.  Some  of 
these  bars  were  42  ft.  in  length,  and  were  kept  from  sagging 
by  wooden  crosspieces  nailed  to  falsework.  The  J^-in.  ver- 
tical face  bars  were  then  hung  from  the  top  and  held  in 
place  in  a  similar  manner.  Next  the  vertical  bars  in  each 
rib  were  placed,  being  stuck  in  the  ground  at  the  bottom  and 
held  at  the  top  by  wire  tied  to  the  scaffolding. 

In  construction,  3  ins.  of  concrete  was  first  placed  above 
the  top  of  the  piles,  the  horizontal  longitudinal  rods  were  put  in 
place,  and  then  the  concreting  carried  tip  throughout  the  whole 
section.  As  the  work  was  .brought  up,  the  horizontal  bars 
in  the  face  and  ribs  were  put  in  place,  care  being  taken  in 
all  cases  to  bed  them  in  fresh  concrete.  The  laps,  where 
the  rods  were  spliced,  were  made  at  the  ribs,  a  2-ft.  lap 
being  used  for  the  base  and  1^-ft.  lap  for  the  face  wall. 
Corrugated  bars  were  used  throughout.  A  1-2-4  mixture  of 
Portland  cement,  sand  and  trap  rock  was  used  for  the  concrete. 
A  fairly  wet  mixture  was  employed,  being  deposited  in  6-in.  lay- 
ers and  thoroughly  tamped. 


ABUTMENTS  AND  RETAINING  WALLS.          317 

SPECIFICATIONS     FOR    REINFORCED     CONCRETE 
RETAINING  WALL. 

The  following  specifications  for  reinforced  concrete  re- 
taining wall  have  been  used  by  the  author  and  show  the 
method  of  construction: 

General. — The  concrete  used  in  reinforced  concrete  must 
be  of  the  classes  called  for  on  the  plan,  or  as  directed  by  the 
engineer,  and  must  be  in  accordance  with  the  general 
specifications  for  .concrete.  It  must  be  mixed,  generally,  to 
the  consistency  known  as  "wet  concrete,"  or  such  that  a 
man  walking  on  same  will  sink  ankle  deep.  The  decision  of 
the  engineer  as  to  the  proper  consistency  of  any  batch  of 
concrete  must  be  binding  upon  the  contractor.  Special  ram- 
mers must  be  used  as  directed  by  the  engineer,  to  properly 
pack  the  concrete  between  and  around  the  steel  bars. 

Workmanship. — Particular  care  must  be  exercised  in  the 
execution  of  reinforced  concrete  work  in  order  to  procure  a 
dense  and  uniform  mixture,  thoroughly  compacted  around 
the  reinforcing  material. 

Reinforcement. — The  contractor  must  furnish  and  embed 
in  the  concrete  round  rods  or  bars  of  dimensions  shown  on 
plans,  wherever  same  are  called  for  by  the  plans,  or  when 
directed  to  do  so  by  the  engineer.. 

The  bars  must  be  of  medium  open-hearth  steel,  in  strict 
conformity  to  Manufacturers'  Standard  Specifications  for 
1903,  and  must  be  in  accordance  with  the  specifications  under 
heading  "Iron  and  Steel." 

The  section  of  the  rod  or  bar  must  be  the  same  as  that 
called  for  on  the  plan.  The  rods  or  bars  must  be  cleaned  of 
all  dirt,  grease  and  other  adhering  substances,  and  must  be 
free  from  rust  and  mill  scale.  In  placing  them  the  direc- 
tions of  the  engineer  must  be  strictly  followed  in  regard  to 
spacing,  position  in  the  cross-section  of  the  concrete,  length, 
laps,  wiring,  bending,  etc. 

In  placing  the  reinforcement  the  following  modus  op- 
erandi  should  be  observed: 

After  the  piles  have  been  driven,  the  ground  properly  lev- 
eled off  and  the  forms  for  the  base  plate  have  been  set  in 
the  ground,  the  4xl2-in.  mesh  American  wire  netting  No.  9 
and  No.  11  mesh  should  be  unrolled  longitudinally  with  the 
abutments  from  one  side  of  the  same  to  the  other  and  con- 
nected properly  with  clips,  stretched  and  attached  to  the  side 
forms.  In  a  similar  manner  the  netting  for  the  two  wing 
walls  should  run  parallel  with  the  outside  face,  lapping  the 
other  netting  12  ins.  and  also  fastened  to  same  with  clipsr 


318  REINFORCED    CONCRETE. 

These  clips  are  furnished  free  with  the  netting.  On  top  of 
this  netting  should  be  located  the  rods  as  shown  in  the  plan 
and  tied  to  same  at  every  fourth  intersection  with  No.  18 
annealed  wire  laid  double,  using  a  No.  8  pair  of  nippers  for 
the  purpose.  While  cutting  the  above  mentioned  netting  in 
lengths,  a  double  set  is  cut  and  laid  ready,  so  as  to  be  pre- 
pared to  place  same  as  soon  as  the  concrete  has  reached 
near  the  top  of  the  slab.  Stakes  should  be  driven  back  of 
the  base  form  with  cross  arms  to  support  the  outmost  rods 
of  the  counterforts  which  are  to  be  embedded  in  the  con- 
crete. The  concrete  is  now  placed  as  rapidly  as  possible  and 
fairly  dry  and  tamped,  and  in  placing,  by  means  of  separate 
hooks  the  lower  wire  netting  is  pulled  and  shook  away  from 
'the  soil,  leaving  a  cover  of  about  \l/t  ins.  to  2  ins.  between 
the  soil  and  the  reinforcement. 

While  this  is  going  on,  the  reinforcing  gang  is  preparing 
for  the  second  layer  of  netting  and  the  top  rods,  and  must 
have  them  all  laid  out  in  the  rotation  in  which  they  are  to 
be  placed.  The  reason  that  the  concrete  in  the  base  plate  is 
to  be  fairly  dry  is  for  the  purpose  of  being  able  to  place  the 
wire  netting  and  rods,  gradually  following  up  the  complete 
concreting.  The  top  concreting  can  commence  at  one  end 
of  the  wing  wall  and  one  end  of  the  abutment,  while  they 
are  still  concreting  the  lower  part  of  the  opposite  end.  Im- 
mediately after  the  top  layer  of  netting  and  rods  is  laid,  the 
oblique  tension  rods  in  the  counterforts  are  stuck  in  the  con- 
crete as  far  down  as  they  can  go  and  stayed  at  the  top  by 
means  of  stay  laths  fastened  to  stakes  driven  in  the  ground 
on  both  sides  of  the  base  plate. 

This  is  done  during  the  top  finishing.  Meanwhile  the 
lumber  and  braces  for  the  front  slab  and  wing  walls  have 
been  made  ready  for  rapid  erection  and  the  4x6-in.  No.  9  and 
No.  11  American  wire  is  placed  horizontally  in  one  length 
around  the  circumference  of  the  wing  walls  and  abutments, 
suspended  at  the  top  from  hooks  or  nails  fastened  to  the 
studs  of  the  front  form,  not  to  the  forms  themselves.  The 
second  layer  of  netting  is  suspended  to  the  first  one  by 
means  of  the  clips  and  so  on  until  the  bottom  is  reached. 
Then  the  rods  are  fastened  to  the  wire  netting  by  means  of 
annealed  wire  at  every  fourth  intersection  until  the  bottom 
is  reached.  When  this  is  done  the  rods  of  the  counterforts 
which  have  been  embedded  in  mortar  are  bent  forward  un- 
til they  are  in  proper  position  and  the  6x6-in.  mesh  No.  9 
and  No.  11  American  wire  is  wired  to  each  set  of  rods  in 
the  counterfort  and  also  wired  to  the  front  netting  and  one 
side  of  the  counterfort  forming  as  erected,  the  other  side 


ABUTMENTS  AND  RETAINING  WALLS.          319 

being  made  in  one  piece  with  the  part  of  the  forms  for  the 
face  slab  running  between  the  counterforts,  in  sections  about 
2  ft.  high.  Then  concreting  can  commence  and  section  by 
section  carefully  spaded,  and  a  somewhat  more  wet  con- 
sistency may  be  used  than  in  the  bottom  slab. 

Any  other  method  of  work  accomplishing  the  same  pur- 
pose— namely:  the  proper  location  of  all  netting  and  all 
rods — may  be  used  at  the  contractor's  discretion,  with  the 
approval  of  the  engineer. 

As  all  rods  of  every  description  are  to  be  hooked  at  least 
1  in.,  it  may  be  added  that  the  corners  of  these  hooks  need 
not  be  square  but  may  be  made  to  a  radius  of  1  in.  All 
splices  of  rods  are  done  by  hooking  both  ends  and  lapping 
them  50  diameters  with  three  ligatures  of  No.  18  annealed 
wire,  and  all  splices  must  break  joints. 

Rods  or  bars  must  be  braced  so  as  not  to  be  displaced  by 
springing  or  by  the  ramming  of  the  concrete.  No  reinforce- 
ment will  be  allowed  within  1  in.  of  any  exposed  surfaces. 
No  concrete  except  the  foundation  course  can  be  placed  un- 
til the  entire  reinforcement  has  been  placed,  wired  and  ap- 
proved by  the  engineer. 

Vertical  and  horizontal  rods  or  bars  shall  be  of  the 
lengths  shown  on  the  plans.  In  beams,  face  slabs  and  floor 
slabs,  the  rods  shall  be  continuous  over  two  supports. 

Loading  and  Risks. — No  vertical  or  heavy  loads  shall  be 
allowed  on  any  reinforced  concrete  structure  within  30  days 
after  the  completion  thereof,  nor  until  such  time  as  the  en- 
gineer may  designate.  The  contractor  will  be  held  respon- 
sible for  any  failure  due  to  faulty  workmanship  or  material, 
premature  loading  or  premature  removal  of  forms. 

Measurement  and  Payment. — The  steel  rods  or  wire  net- 
ting or  bars  shall  be  paid  for  at  the  unit  price  per  pound  or 
per  square  foot  named  in  the  contract.  Payment  will  be 
made  upon  the  estimated  weight  of  rods  and  bars  computed 
upon  the  basis  of  490  Ibs.  per  cu.  ft.,  for  the  lengths  and 
cross  sections  indicated  on  the  plans  or  placed  by  order  of 
the  engineer.  If  bars  of  larger  cross  section  than  called  for 
are  used  the  excess  shall  not  be  paid  for.  No  allowances 
will  be  made  for  waste  or  laps,  except  where  laps  are  shown 
on  plans,  or  made  by  direction  of  the  engineer.  The  unit 
price  per  pound  must  include  the  furnishing,  bending,  plac- 
ing and  wiring  of  the  rods  or  bars,  and  all  labor,  tools,  wire, 
and  other  material  necessary  to  complete  the  work. 

Reinforced  concrete,  exclusive  of  the  reinforcing  material 
shall  be  paid  for  at  the  unit  prices  named  in  the  contract,  and 
no  deduction  will  be  made  tor  the  volume  of  concrete  dis- 
placed by  the  steel. 


CHAPTER  V. 

CULVERTS,   CONDUITS,   SEWERS,   PIPES,  AND  DAMS 
ARCH  CULVERTS. 

For  arch  culverts  the  design  is  made  the  same  as  for 
arches  in  bridge  construction,  the  elastic  theory  forming  the 
basis.  If  extradosal  and  intradosal  reinforcement  is  em- 
ployed, it  is  not  necessary  that  the  pressure  line  comes  within 
the  middle  third,  and  therefore  quite  light  constructions  may 
be  made  with  safety.  The  thrust  from  the  arch  is  trans- 
ferred to  the  base  by  means  of  buttresses,  which  thus  with 
the  comparatively  thin  face  walls  and  the  base  replace  the 
heavy  abutments  in  masonry  construction.  Culverts  are  built 
with  or  without  inverts  according  to  the  stability  of  the  soil 
and  the  local  conditions. 

BOX  CULVERTS. 

Box  culverts  are  calculated  like  floor  slabs.  The  follow- 
ing method  of  rinding  the  pressure  on  a  box  culvert  is  based 
upon  the  method  outlined  by  Mr.  W.  W.  Colpitts,  C.  E.,  in 
"Railway  Age,"  Aug.,  1907: 

Assumptions. — The  live  load  is  taken  at  10,000  Ibs.  per 
linear  foot  of  track  uniformly  distributed  by  the  ties  over  8 
ft.  width  of  roadway.  The  further  distribution  of  the  load 
downwards  is  based  upon  the  unfavorable  assumption  that 
the  zero  load  line  follows  a  slope  of  5^  to  1. 

Design  of  Covers  for  Box  Culverts. — Let  DL  =  dead  load 
per  sq.  ft.  on  a  plane  h  ft.  from  the  base  of  rail. 

320 


CULVERTS,  CONDUITS,  SEWERS,  DAMS.          321 

g  =  weight  of  fill  per  cu.  ft. 
Then  L>L  =  gh. 

LL  =  live  load  in  Ibs.  per  sq.  ft. 

Q  =  DL  +  LL. 
For  g  —  100  Ibs.,  we  have: 
DL  —  100  A,  or  for  a  factor  of  safety  of  2  for  the  dead 

load, 
DL  =  200  h. 

20  000 
LL  =     .  '  lfi   for  a  10,000  Ibs.  train  load. 

Taking  an  impact  of  50  per  cent  and  a  factor  of  safety  of  4 
for  the  live  load,  we  have: 

120,000 

"   h+  16 

and  Q  =  DL  +  LL  =  200 


Then  we  have  M  =  ^12  =  300 1*  (^r^j  +  *) (47) 

where  /  is  the  span  of  the  culvert  in  feet. 

For  n  =  15,  and  p  =  0.0072,   we  find  by  interpolation  in 
Table  XXXIX, 

k  =  0.369. 

Therefore  A»  =  0.0072  X  12  X  d  =  0.086  d (48) 

Assuming  fo  =  2,300  Ibs.  per  sq.  in.   (ultimate),  and  substi- 
tuting in  Formula  (10), 

M  =  H  fe    (1  —  */3)  bd* 
we  get 

M 


^  =      40 (49) 

where  M  represents  the  ultimate  moment. 

Diagram  for  the  Design  of  Covers  for  Box  Culverts.— In 

Fig.  130,  plotted  from  Formulas  (47),  (48)  and  (49),  Curve  A 
gives  the  theoretical  thickness  of  cover  for  various  spans  under 
banks  between  30  and  40  ft.  high.  Curve  a  gives  the  area  of 


322 


REINFORCED   CONCRETE. 


steel   reinforcement  per  linear  foot  of  cover  for  banks  between 
30  and  40  ft.  high.     Curves  B  and  b  and  Curves  C  and  c  corre- 


qmooo 


Fig.   130. — Diagram  for  the  Design  of  Covers  for    Box  Culverts. 

spond  to  the  above  under  banks  respectively  22  to  30  ft.  high 
and  0  to  22  ft.  high. 


CULVERTS,  CONDUITS,  SEWERS,  DAMS. 


323 


Each  curve  is  calculated  for  the  maximum  height  of  bank 
shown.  To  the  theoretical  thickness  of  the  cover,  d,  should  be 
added  from  1%  to  3  ins.,  sufficient  to  embed  the  bars. 

Design  of  Sides  of  Box  Culverts.  —  For  the  sides  of  box 
culverts  the  resultant  horizontal  pressure  on  the  walls  is  ap- 
proximately 


and  the  horizontal  pressure  at  base  of  wall  in  Ibs.  per  sq.  ft.  is 


pr         I* 

^    -  2 


P  =  p> 


60,000 
/*  +  16 


+    100  h 


(50) 


in  Ibs.  per  sq.  ft.  applied  over  the  entire  surface  of  the  side  wall 
of  the  culvert. 

Diagram  for  the  Design  of  Sides  of  Box  Culverts.  —  Fig. 
131  is  plotted  from  Formulas  (47),  (48)  and  (50).    Curve  D  is 


x"f 


& 


J"'  /O'  ~7sr 

Depth  Bottom?  0f  Cwer  to  Top  0f  Base 

Fig.   131.— Diagram  for  the  Design  of  Sidewalls  for  Box  Culverts. 


324  REINFORCED    CONCRETE. 

used  when  the  bank  is  between  30  and  40  ft.  high  and  gives  the 
theoretical  thickness  for  various  spans.  Curve  d  is  used  when 
the  bank  is  between  30  and  40  ft.  high  and  gives  the  area  of 
steel  reinforcement  per  lin.  ft.  of  side  wall,  while  curves  E  and 
e  and  curves  F  and  /  correspond  to  the  above  under  banks  re- 
spectively 20  to  30  ft.  high  and  0  to  20  ft.  high,  each  curve  being 
calculated  for  the  maximum  height  of  bank.  As  in  Fig.  130,  the 
thickness  of  the  side  wall,  d,  should  be  increased  1%  to  3  ins., 
sufficient  to  embed  the  bars. 

It  is  customary  to  put  either  brackets  or  braces  in  the  cor- 
ners to  take  care  of  unequal  pressures.  The  side  rods  should  be 
bent  inward  at  the  top  and  extend  through  the  thickness  of  both 
top  and  bottom.  All  rods  should  be  hooked  at  each  end. 

When  the  fill  comes  below  3  ft.  above  the  top  of  culvert  the 
impact  is  figured  at  100  per  cent,  and  for  large  spans  the  live 
loads  are  assumed  to  be  concentrated. 

Cost  of  Concrete  Culverts.—  Mr.  Colpitts*  gives  the  follow- 
ing cost  of  retaining  walls,  abutments  and  box  culverts,  for  the 
permanent  way  of  the  Kansas  City  Outer  Belt  &  Electric  Ry. 
These  figures  are  of  particular  interest,  for  the  variation  in 
prices  of  materials  during  the  two-year  period  while  work  was 
in  progress  and  as  giving  the  average  cost  of  the  work  on  the 
whole  line  as  well  as  for  individual  structures.  The  culverts 
were  all  box  culverts  with  wing  walls  and  the  abutments  were 
for  girder  bridges.  Walls  and  abutments  were  of  L  section 
with  triangular  or  trapezoidal  counterforts  at  the  back  between 
base  slab  and  coping.  The  form  work  was  thus  rather  complex. 
All  work  was  reinforced  concrete,  and  was  done  by  contract 
under  the  following  conditions :  The  work  of  preparing  founda- 
tions, including  excavation,  pile  driving,  diversions  of  streams, 
etc.,  was  done  by  the  railroad  company,  which  also  bore  one-half 
the  cost  of  keeping  foundations  dry  while  forms  were  being 
built  and  concrete  placed.  The  railroad  company  also  furnished 
the  reinforcing  bars  at  the  site  of  each  opening.  The  concrete 
work  was  let  at  $9  per  cu.  yd.,  which  figure  covered  all  the  labor 
and  materials  necessary  to  complete  the  work,  other  than  the 
*Railway  Age,  Aug.  2,  1907. 


CULVERTS,  CONDUITS,  SEWERS,  DAMS.  325 

exceptions  mentioned.  The  concrete  proportions  were  1-3-5. 
The  cement  used  was  lola  Portland  and  Atlas  Portland.  The 
sand  was  obtained  from  the  bed  of  the  Kansas  River  in  Kansas 
City.  The  rock  used  was  crushed  limestone,  passing  a  2-in.  ring 
and  freed  from  dust  by  screening.  Corrugated  reinforcing  bars, 
having  an  elastic  limit  of  from  50,000  to  60,000  Ibs.  per  sq.  in., 
manufactured  by  the  Expanded  Metal  &  Corrugated  Bar  Co.  of 
St.  Louis,  Mo.,  were  used  exclusively.  The  concrete  in  the 
smaller  structures  was  mixed  by  hand,  in  the  larger  by  a  No.  1 
Smith  mixer.  In  the  first  structures  built  2-in.  form  lumber  was 
used,  with  2x6-in.  studs  placed  3  ft.  on  centers.  This  was 
abandoned  later  for  1-in.  lumber  with  2x6-in.  studs,  12  ins.  on 
centers,  and  was  found  to  be  more  satisfactory  in  producing  a 
better  face.  The  structures  were  built  in  the  period  from 
April,  1905,  to  May,  1907.  Costs  and  wages  were  as  follows : 

Cement — 

Per  barrel  at  structure,  April,  1905 $1.25 

Per  barrel  at  structure,  April,  1907 1.92 

Average  cost  per  barrel  at  mill 1.42 

Freight   per   barrel 0.21 

Hauling  iVz  miles  and  storage 0.12 

Average  cost  at  structure 1.75 

Average  cost  per  cu.  yd.  concrete  (1.1  bbls.) 1.93 

Sand — 

Per  cu.  yd.  at  structure,  April,  1905 $0.625 

Per  cu.  yd.  at  structure,  April,  1907 0.75 

Average  cost  per  cu.  yd.,  river  bank 0.30 

Freight  per  cu.  yd 0.22 

Hauling   IV-2   miles 0.20 

-Average  cost  at  structure 0.72 

Average  cost  per  cu.  yd.  concrete  (Ms  cu.  yd.) 0.36 

Stone — 

Per  cu.  yd.  at  structure,  April,  1905 $  1.10 

Per  cu.  yd.  at  structure,  April,  1907 1.75 

Average  cost  per  cu.  yd.  at  crusher 0.65 

Hauling  4  miles 0.84 

Average  cost  at  structure 1.49 

Average  cost  per  cu.  yd.  concrete  (0.9  cu.  yd.) 1.34 


326  REINFORCED    CONCRETE. 

Lumber — 

Per  M.  ft.  at  structure,  April,  1905 $15.00 

Per  M.  ft.  at  structure,  April,  1907 22.50 

Average  cost  per  M.  at  structure 19.00 

Average  cost  per  cu.  yd.  concrete 0.49 

Labor —  Max.  Min. 

Common  labor,  cts.  per  hour 20  17 

Carpenters,  cts.  per  hour 40  30 

With  these  prices  and   wages   the   average   cost  of  concrete 
work  for  the  whole  line  was : 

Item.  Per  cu.  yd. 

Form  building  and  removing $1.98 

Mixing  and  placing  concrete 0.74 

Placing  reinforcement 0.10 

Wire,  nails,  water,  ttc 0.20 

1.1  bbls.  cement  at  $1.75 1.93 

%  cu.  yd.  sand  at  $0.72 0.36 

0.9  cu.  yd.  stone  at  $1.49 1.34 

Lumber  for  forms 0.49 

Total   .$7^14 

The   following  are   the   costs   of   specific   structures   built   at 
different  times : 

Example  /.—Indian  Creek  Culvert.     14x15  ft.,  250  long,  com- 
pleted November,  1905: 

Percu.  yd. 

Cement $1.37 

Sand    34 

Stone    1.10 

Labor    2.48 

Lumber     76 

Miscellaneous    18 

Total $6.23 

Example  II. — Third    Street  Abutments   and  Retaining  Wall. 
Completed  November,  1906: 

Per  cu.  yd. 

Cement   $1-78 

Sand    35 

Stone     1.35 

Lumber   74 

Labor    •. 2.75 

Miscellaneous 16 

Total   .  $7.13 


CULVERTS,  CONDUITS,  SEWERS,  DAMS.          327 

Example  III. — Abutments,  Overhead  Crossing  with  Union 
Pacific  and  Rock  Island.  Completed  May,  1007: 

Per  cu.  yd. 

Cement    $1.92 

Sand    32 

Stone    1.74 

Lumber    98 

Labor    2.96 

Miscellaneous     16 

Total    $8.08 

EXAMPLES  OF  ARCH  CULVERTS. 

Reinforced  concrete  culverts  have  been  adopted  as  standard 
by  several  American  railroads,  and  while  practical  experience 
may  tend  to  reduce  dimensions  more  in  conformity  with  theoreti- 
cal research  and  foreign  practice,  a  few  examples  will  illustrate 
recent  application  of  concrete  steel  in  culvert  construction. 


_  Top  of  Tie 


Fig.  132.— Standard  Arch  Culverts  for  Inside  Dimensions  of  4x4  ft., 
5x5  ft.,  and  6x6  ft.,  C.,  B.  &  Q.  Ry. 

Standard  Arch  Culverts,  C.,  B.  &  Q.  R.  R.— Fig.  132  illus- 
trates standard  arch  culverts  adopted  by  the  C.,  B.  &  Q.  R.  R., 
in  which 

L=-^h  +  x  +  4:it (51) 

-where  x  =  width  of  the  roadbed  at  the  crown,  the  other  quanti- 
ties being  as  shown  in  Fig.  132. 

Table  LXV  gives  various  dimensions  for  this  type  of  culvert. 


328 


REINFORCED    CONCRETE. 


TABLE  LXV. — DIMENSIONS  AND  MATERIALS  FOR  STANDARD  ARCH 
CULVERTS,  C.,  B.  &  Q.  R.  R. 


Inside 

Length  of 

Cu.  yds. 

Cu.  yds. 

Lbs.  metal, 

Lbs.  metal, 

dimensions 

wing  walls, 

concrete 

lin.  ft.  of  " 

wing  walls. 

lin.  ft.  of 

in  feet. 

ft.  ins. 

wing  walls. 

barrel. 

barrel. 

4x4 

5-3 

6 

0.5 

236 

54 

5x5 

6-11 

10 

0.71 

401.7 

76.7 

6x6 

8-6 

12 

1.00 

553.5 

103.4 

Arch  Culvert,  Kalamazoo,  Mich. — Fig.  133  illustrates  a 
culvert  of  9  ft.  10  ins.  span  and  1,080  ft.  long  built  at  Kalamazoo, 
Mich.  The  reinforcement  consists  of  woven  steel  wire  fabric 
of  No.  11  wire  laid  in  two  layers  each,  at  the  intrado,  extrado 
and  invert  as  indicated  in  the  drawing.  The  total  length  of 


Fig.  133.— Arch  Culvert  at  Kalamazoo,  Mich. 

fabric  surrounding  the  culvert  in  one  section  is  175  ft.  There 
is  an  average  of  5  wires  per  linear  foot  enclosing  the  culvert  ex- 
cept where  the  inner  and  outer  reinforcement  overlaps.  The 
bearing  portion  of  the  concrete  in  the  inverted  arch  was  changed 
in  form  as  shown  in  the  drawing  by  dotted  lines,  according  to 
the  character  of  the  soil.  Where  quicksand  was  encountered  two 


CULVERTS,  CONDUITS,  SEWERS,  DAMS.          329 

6-in.  tile  drains  were  laid  under  the  invert  and  these  by  remov- 
ing the  excess  of  water  from  the  quicksand  made  it  a  firm  and 
good  foundation.  The  use  of  a  wire  fabric  as  reinforcement  is  a 
safeguard  against  mistakes  or  omissions  in  placing  the  reinforce- 
ment during  construction. 

Arch  Culvert,  Great  Northern  Ry. — A  reinforced  concrete 
arch  culvert  of  large  span*  is  shown  in  Fig.  134.  The  plans 
were  calculated  for  heights  of  bank  of  both  22  and  40  ft.,  weight 
of  fill  being  taken  at  100  Ibs.  per  cu.  ft.  A  uniform  live  load  of 
10,000  Ibs.  per  lin.  ft.  of  track  was  assumed,  50  per  cent  added 
for  impact,  a  factor  of  safety  of  4  used  on  such  live  load  plus 
impact,  and  of  2  on  dead  load.  The  figures  for  the  ultimate 
strength  of  concrete  in  tension,  compression  and  shear  were 
200,  2,000,  and  400  Ibs.  respectively.  Modulus  of  elasticity  of 
concrete  in  compression  was  taken  at  3,000,000  Ibs.  per  sq.  in., 
elastic  limit  of  the  corrugated  bar  reinforcement,  50,000  Ibs.  pet 
sq  in.,  and  weight  of  concrete,  150  Ibs.  per  cu.  ft. 

It  was  found  that  the  plans  shown  in  Fig.  134  could  be  used 
for  a  fill  of  50  or  even  60  ft.  without  changing  them  appreciably. 
It  was  also  found  that,  so  far  as  quantities  are  concerned,  rein- 
forced concrete  arch  culverts  are  more  economical  than  those 
of  the  box  pattern  for  any  span  exceeding  6  ft.  The  form  work 
for  an  arch  culvert  is  more  expensive  than  for  one  of  the  box 
shape,  but  the  extra  expense  is  not  believed  to  be  large  enough  to 
justify  the  adoption  of  the  latter  style  of  structure  for  spans  ex- 
ceeding 6  ft. 

Table  LXVI  contains  quantities  of  concrete  and  steel  for 
culverts  similar  to  Fig.  134,  also  for  pipe  and  box  culverts.  As 
compared  with  quantities  contained  in  plain  concrete  culverts  as 
commonly  built  and  accepted  as  good  practice  in  this  country,  a 
marked  difference  is  seen  to  exist.  Thus,  the  8x8  ft.  reinforced 
concrete  arch  culvert,  contains  1.37  cu.  yds.  of  concrete 
and  158  Ibs.  of  steel  per  linear  foot  of  barrel,  which  steel,  fig- 
ured at  3%  cts.  in  place,  is  equivalent  to  0.69  cu.  yd.  of  concrete 
when  the  latter  is  taken  at  $8.00  per  cu.  yd.  in  place.  The  total 
equivalent  concrete  yardage  is  then  1.37  +  0.69  =  2.06  cu.  yds. 

*C  F.  Graff,  C.  E..  Engineering  News.  Vol.  LV,  No.  1. 


330 


REINFORCED    CONCRETE. 


per  lin.  ft.  of  barrel.  As  against  this  we  have  in  plain  concrete 
culverts  of  the  same  span  and  of  usual  standard  designs  from  3 
to  4  cu.  yds.  Also,  in  this  particular  culvert,  one  pair  of  wing 
walls  is  observed  to  contain  11.22  cu.  yds.  of  concrete  and  793 
Ibs.  of  steel,  or  a  total  equivalent  concrete  quantity  of  11.22  4- 
3.47  =  14.69  cu.  yds.  of  concrete,  as  against  40  to  50  cu.  yds.  in 
ordinary  plain  concrete  construction. 


Part     Plan. 

Fig.    134.— Reinforced    Concrete    Arch    Culvert    of   20-Ft.    Span. 


TABLE  LXVI. — DIMENSIONS  AND  MATERIALS  FOR  REINFORCED  CONCRETE 
CULVERTS,  G.  N.  Ry. 


Size, 
ft.     in. 

Barrel  per  lin.  ft. 

One  Pair  Wing  Walls. 

Remarks. 

Concrete 
cu.  yds. 

Steel, 
pounds. 

Paving, 
cu.  yds. 

Concrete 
cu.  yds. 

Steel, 
pounds. 

Paving, 
cu.  yds. 

2x    0 
3x    0 
4x    0 
4x    4 
4x    6 
6x    6 
8x    8 
12x12 
17x16 
16x20 
16x20 

0.10 
0.23 
0.30 
0.54 
0.72 
0.86 
1.37 
2.78 
3.70 
5.00 
5.05 

5 
10 
12 

61 
73 
116 
158 
237 
287 
300 
307 

Pipe  Culvert 

Box 
Arch 

M 

2.38 
2.50 
5.16 
11.22 
37.25 
51.80 
45.60 
46.02 

141 

128 
397 
793 
1,850 
2,579 
2,143 
2,277 

"26!  2" 

0.66 

CULVERTS,  CONDUITS,  SEWERS,  DAMS. 


331 


EXAMPLES   OF  BOX  CULVERTS. 

Standard  Box  Culverts,  C.,  B.  &  Q.  R.  R.— Fig.  135  and 

Table  LXVII  give  dimensions  and  quantities  of  materials  for 

culverts  from  4x4  ft.  to  7x8  ft.,  inside  dimensions,  and  Fig.  136 

and  Table  LXVIII  give  similar  data  for  box  culverts  from  8x6 

TABLE  LXVII. — DIMENSIONS  AND  MATERIALS  FOR  STANDARD  Box 
CULVERTS,  C.,  B.  &  Q.  R.  R. 


Inside 
dimens. 

Length  of 
wing  walls, 

Cu.  yds. 
concrete 

Cu.  yds. 
concrete 

1i«       f+ 

Thickness, 
side  walls, 

Thickness, 
roof  slab, 

Thickness, 
floor  slab 

in  ft. 

ft.  and  ins. 

wing  walls. 

Jin.  it. 
barrel. 

in  ins. 

in  ins. 

in  ins. 

4x4 

5    10 

7.4 

0.75 

12 

12 

12 

4x5 

7    6 

9.2 

0.83 

12 

12 

12 

4x6 

9    2 

11.6 

0.9 

12 

12 

12 

5x4 

6    1 

9.0 

0.91 

12 

14 

14 

5x5 

7    9 

11.3 

0.99 

12 

14 

14 

5x6 

9    6 

13.9 

.06 

12 

14 

14 

6x5 

8    0 

13.5 

.18 

12 

16 

16 

6x6 

8    0 

16.5 

.25 

12 

16 

16 

6x8 

12    9 

18.3 

.60 

15 

16 

16 

7x5 

8    4 

15.65 

.39 

12 

18 

18 

7x7 

11    5 

24.9 

.72 

15 

18 

18 

7x8 

13    0 

29.13 

•  1.82 

15 

18 

18 

TABLE  LXVIII. — DIMENSIONS  AND  MATERIALS  FOR  STANDARD  Box 
CULVERTS,  C.,  B.  &  Q.  R.  R. 


Inside 
dimens. 
in  ft. 

Length  of 
wing  walls  , 
ft.  and  ins. 

Cu.  yds. 
concrete 

wing  walls. 

Cu.  yds. 
concrete 
lin.  ft.  of 
barrel. 

Thickness, 
side  walls, 
in  ins. 

Thickness, 
roof  slab, 
in  ins. 

Thickness, 
floor  slab, 
in  ins. 

8x6 
8x8 
8x  10 
10x10 
10x12 

10    0 
13    4 
10    5 
17    0 
20    4 

31.0 
39.7 
57.1 
62.3 
76.0 

1.89 
2.08 
2.51 
3.07 
3.3 

15 
15 
18 
18 

18 

20 
20 
20 
24 

24 

20 
20 
20 
24 

24 

ft.  to  10x12  ft.  inside  dimensions,  as  adopted  by  the  C,  B.  &  Q. 
R.  R.    In  Table  LXVII,  the  formula  for  L  is  as  follows : 

10 
L=  3h  + 


3ft. 


(52) 


332 


REINFORCED    CONCRETE. 


Fig.    135.— Standard  Box  Culvert  for  Clear  Widths  of  1   ft.,   C.,  B 
&  Q.  Ry. 


x'  K--  A 

'  5MXv 

J"    -$  : 

^^ 

|  Ry.M.8,6. 

^ 

1 

K  y 

*t 

Fig.    136.— Standard    Box   Culvert   for   Clear   Widths    of  8   Ft.   and 
over,    C.,   B.   &   Q.    Ry. 

CONDUITS,  SEWERS  AND  PIPES. 

Erosive  and  Transporting  Powers  of  Water. — The  erosive 
power  of  water,  or  its  power  of  overcoming  cohesion,  varies  as 
the  square  of  the  velocity  of  the  current 

The  transporting  power  of  a  current  varies  as  the  sixth  power 
of  the  velocity. 

Hence  a  current  running  3  ft.  per  second  or  about  2  miles 
per  hour,  will  carry  fragments  of  stone  the  size  of  a  hen's  egg 
or  about  3  oz.  in  weight.  A  current  of  3  miles  an  hour  will 
carry  fragments  of  IVz  tons,  and  a  current  of  20  miles  an  hour 
will  carry  fragments  of  100  tons. 

The  transporting  power  of  water  must  not  be  confounded 
with  i':s  erosive  power.  The  resistance  to  be  overcome  in  the 
one  case  is  weight,  in  the  other  cohesion ;  the  latter  varies  as  the 
square,  the  former  as  the  sixth  power  of  the  velocity. 

Resistance  of  Soil  to  Erosion  by  Water. — Prof.  W.  A.  Burr 
in  "Engineering  News,"  Feb.  8,  1894,  gives  a  diagram  showing 
the  resistance  of  various  soils  to  erosion  by  flowing  water.  The 
following  figures  show  the  comparative  resistance; 


CULVERTS,  CONDUITS.  SEWERS,  DAMS.          333 

Pure  sand  resists  erosion  by  flow  of  1.1  ft.  per  second. 
Sand  soil,  15  per  cent  clay,  1.2  ft.  per  second. 
Sandy  loam,  40  per  cent  clay,  1.8  ft.  per  second. 
Loamy  soil,  65  per  cent  clay,  3  ft.  per  second. 
Clay  loam,  85  per  cent  clay,  4.8  ft.  per  second. 
Agricultural  clay,  95  per  cent  clay,  6.2  ft.  per  second. 
Clay,  7.35  ft.  per  second. 

Kutter's  Formula. — Kutter's  formula  for  velocity  of  water 
in  conduits  is  as  follows : 


v 


1.811  0.00281 

-  +  41.6  +  — 


41.6  +  0.0028U       n 


(53) 


in  which 

v  =  mean  velocity  in  ft.  per  second 

a 
r  =  —  =  hydraulic  mean  depth  in  feet 

a  =  area  of  cross  section  in  sq.  ft. 
p  =  wetted  perimeter  in  linear  feet 

s  =-j-  =  sine  of  slope,  or  the  fall  of  a  given  distance  divided 

by  said  distance. 
n  =  a  coefficient,  depending  on  the  nature  of  the  lining  01 

surface  of  the  channel 
If  we  call 

1.811  0.00281 

"~       +  41.6  +  •       ~ 


.6  +  0.00281\   n 
we  have 


(54) 

which  is  Chezy's  formula.     Table  LXIX  for  the  flow  of  water 
in  pipes  is  based  upon  Kutter's  formula. 

Since  n  varies  with  the  roughness  of  the  surface  of  the  chan- 


334 


REINFORCED    CONCRETE. 


TABLE  LXDL — FLOW  OF  WATER  IN  CIRCULAR  PIPES,  SEWERS,  ETC,, 

FLOWING  FULL. 

Based  on  Kutter's  Formula,  with  n=  .013. 

Slope  is  head  divided  by  length  of  pipes. 

(From  Kent.) 


Diam. 

Discharge  in  cubic  feet  per  second  for  varying  slopes. 

Slope  .  .  . 

1  in  ICO  1  in  200 

1  in  300 

1  in  400 

1  in  500 

1  in  600 

1  in  700 

1  in  800 

15  n.  ... 

6.18 

4.37 

3.57 

3.09 

2.77 

2.52 

2.34 

2.19 

16  *   .. 

7.38 

5.22 

4.26 

3.69 

3.30 

3.01 

2.79 

2.61 

18  '   .. 

10.21 

7.22 

5.89 

5.10 

4.56 

4.17 

3.86 

3.61 

20  '   .. 

13.65 

9.65 

7.88 

6.82 

6.10 

5.57 

5.16 

4.83 

22  '   .. 

17.71 

12.52 

10.22 

8.85 

7.92 

7.23 

6.69 

6.26 

Slope  .  . 

1  in  200 

1  in  400 

1  in  600 

1  in  800 

1  in  1000 

1  in  1250 

1  in  1500 

1  in  1800 

2  ft.  0  in. 

15.88 

11.23 

9.17 

7.94 

7.10 

6.35 

5.80 

5.29 

2  "  2  " 

19.73 

13.96 

11.39 

9.87 

8.82 

7.89 

7.20 

6.58 

2  .,  4  .. 

24.15 

17.07 

13.94 

12.07 

10.80 

9.66 

8.82 

8.05 

2  "  6  " 

29.08 

20.56 

16.79 

14.54 

13.00 

11.63 

10.62 

9.69 

2  "  8  " 

34.71 

24.54 

20.04 

17.35 

15.52 

13.88 

12.67 

11.57 

Slope  .  . 

1  in  500 

1  in  750 

1  in  1000 

1  in  1250 

1  in  1500 

1  in  1750 

1  in  2000 

1  in  250Q 

2ft.lOin. 

25.84 

21.10 

18.27 

16.34 

14.92 

13.81 

12.92 

11.55 

3  "  0  " 

30.14 

24.61 

21.31 

19.06 

17.40 

16.11 

15.07 

13.48 

3  "  2  " 

34.90 

28.50 

24.68 

22.07 

20.15 

18.66 

17.45 

15.61 

3  "  4  " 

40.08 

32.72 

28.34 

25.35 

23.14 

21.42 

20.04 

17.93 

3  "  6  " 

45.66 

37.28 

32.28 

28.87 

26.36 

24.40 

22.83 

20.41 

Slope  .  . 

1  in  500 

1  in  705 

1  in  1000 

1  in  1250 

1  in  1500 

1  in  1750 

1  in  2000 

1  in  2500 

3  ft.  8  in. 

51.74 

42.52 

36.59 

32.72 

29.87 

27.66 

25.87 

23.14 

3  "  10  " 

58.36 

47.65 

41.27 

36.91 

33.69 

31.20 

29.18 

26.10 

4  "  0  " 

65.47 

53.46 

46.30 

41.41 

37.80 

34.50 

32.74 

29.28 

4  "  6  " 

89.75 

73.28 

63.47 

56.76 

51.82 

47.97 

44.88 

40.14 

6  "  0  " 

118.9 

97.09 

84.08 

75.21 

68.65 

63.56 

59.46 

53.18 

Slope  .  . 

1  in  750 

1  in  1000 

1  in  1500 

1  in  2000 

1  in  2500 

1  in  3000 

1  in  3500 

1  in  4000 

5  ft.  6  in, 

125.2 

108.4 

88.54 

76.67 

68.58 

62.60 

57.96 

54.21 

6  "  0  " 

157.8 

136.7 

111.6 

96.66 

86.45 

78.92 

73.07 

68.35 

6  "  6  " 

195.0 

168.8 

137.9 

119.4 

106.8 

97.49 

90.26 

84.43 

7  "  0  " 

327.7 

205.9 

168.1 

145.6 

130.2 

118.8 

110.00 

102.9 

7  "  6  " 

285.3 

247.1 

201.7 

174.7 

156.3 

142.6 

132.1 

123.5 

Slope  .  . 

1  in  1500 

1  in  2000 

1  in  2500 

1  in  3000 

1  in  3500 

1  in  4000 

1  in  4500 

1  in  5000 

8  ft.  0  in. 

239.4 

207.3 

195.4 

169.3 

156.7 

146.6 

138.2 

131.1 

8  "  6  " 

281.1 

243.5 

217.8 

198.8 

184.0 

172.2 

162.3 

154.0 

9  "  0  " 

327.0 

283.1 

253.3 

231.2 

214.0 

200.2 

188.7 

179.1 

9  "  6  " 

376.9 

326.4 

291.9 

266.5 

246.7 

230.8 

217.6 

206.4 

10"  0  " 

431.4 

373.6 

334.1 

305.0 

282.4 

264.2 

249.1 

236.3 

For  U.  S.  gallons,  multiply  the  figures  in  the  table  by  7.4805. 

For  a  given  diameter  the  quantity  of  flow  varies  as  the  square  root  of  the 
sane  of  the  slope.  By  using  this  principle  the  flow  for  other  slopes  than  those 
given  in  the  table  may  be  found 


CULVERTS,  CONDUITS,  SEWERS,  DAMS.          335 


nel,  we  are  here  interested  only  in  that  value  of  n  relating  to 
concrete.    The  value  is 

n  =  0.013, 
which  gives  the  values  in  Table  LXX  for  c,  when 

s  >  0.001, 

From  this  table  the  velocity,  and  hence  the  quantity,  of  water 
flowing  in  any  pipe  may  be  determined. 

TABLE  LXX. — VALUES  FOR  c  IN  CHEZY'S  FORMULA. 
(From  Kent.) 

n  =  0.013. 


Diam.  in  ft. 

c 

Diam.  in  ft. 

c 

0.5 

69.5 

8. 

130.4 

1.0 

85.3 

9. 

132.7 

1.5 

94.4 

10. 

134.5 

2. 

101.1 

11. 

136.2 

3. 

110.1 

12. 

137.7 

4. 

116.5 

14. 

140.4 

5. 

121.1 

16. 

142.1 

6. 

124.8 

18. 

144.4 

7. 

127.9 

20. 

146. 

Grade  of  Sewers. — The  correct  limit  of  grades  which  can 
be  flushed,  0.1  to  0.2  per  cent,  may  be  assumed  for  sewers 
which  are  sometimes  dry,  while  0.3  per  cent  is  allowable  for  the 
trunk  sewers  in  large  cities.  Sewers  should  run  dry  as  rarely 
as  possible. 

Calculations. — For  conduits  the  calculations  are  somewhat 
complex  owing  to  varying  conditions  and  uncertain  stresses,  as 
consideration  must  be  given  to  eventual  future  superimposed 
loads.  The  maximum  live  load  with  its  impact  in  addition  to 
the  weight  of  the  backfill  should  be  taken  to  find  the  maximum 
stress,  although  the  actual  stress  in  most  cases  will  be  consid- 
erably less.  Here  the  judgment  of  the  designer  must  be  used. 

Calculation  for  Internal  Pressure.— For  internal  pressure 
the  calculation  is  as  follows : 


336  REINFORCED    CONCRETE. 

Let  po  =  internal  pressure  Ibs.  per  sq.  in. 
d  :=  diameter  of  conduit  in  inches. 

As  =  area  of  steel  reinforcement  per  lin.  ft.  in  sq.  in. 

/8  =  unit  stress  in  steel  reinforcement. 
If  concrete  is  to  take  no  part  of  the  tension,  we  have 


_  pod 
or  AS  —  2f 

Longitudinal  reinforcement  is  provided  for  bending  and  tem- 
perature stresses.  For  bending  moments  the  pipe  is  calculated 
like  a  beam  and  for  temperature  stresses  the  author  allows 
about  1/500  of  the  area  of  the  shell  similarly  as  for  retaining 
walls,  but  for  conduits  the  range  of  maximum  and  minimum 
temperature  is  considerably  less.  For  small  pipes  running  over 
a  long  distance,  expansion  joints  should  be  provided  similar  to 
those  in  use  for  iron  pipes,  particularly  where  the  back  fill  is 
shallow  and  the  range  of  temperature  great. 

Calculation  for  External  Pressure.  —  For  large  pipes  or 
conduits  the  regular  arch  calculation  becomes  necessary,  where- 
by the  pressure  line  is  traced  and  abutments  determined. 

For  smaller  pipe  it  has  been  found  sufficient  to  calculate  the 
external  live  and  dead  load  per  linear  foot  and  make  the  com- 
bined thickness  of  the  two  sides  of  the  shell  sufficiently  large  so 
that  the  resulting  compression  is  taken  by  the  concrete  alone. 
Reinforcement  in  the  form  of  a  fabric  or  a  rod  netting  is  then 
added  to  provide  for  bending  moments  and  temperature  stresses 

Myer's  Formula.  — 


A=  area  of  waterway  in  sq.  feet. 
M—  area  drained,  in  acres. 

c=  1  as  a  minimum  for  flat  country. 

£—  1.6  for  a  hilly  compact  ground. 

c=  4.   as   a  maximum   for  mountains. 


CULVERTS,  CONDUITS,  SEWERS,  DAMS.          337 
Talbot's    Formula.— 


notations  as  above,  c  as  stated  below. 

This  formula  is  not  intended  for  use  for  drainage  area 
larger  than  400  sq.  miles.  It  was  derived  with  special  ref- 
erence to  areas  under  77  sq.  miles. 

c:  For  rolling  country  subject  to  floods  during  melting 
snow,  and  with  a  length  of  valley  3  or  4  times  the  width 
let  c  =  ft. 

In  districts  not  affected  by  snow,  or  where  length  of 
valley  is  several  times  the  width  let  c  =  1-5  to  1-6. 

For  steep  slopes,  increase  c. 

Latham's  Rule.— 

/=-^ 
100 

d=  depth  of  excavation. 
r=  external  radius  of  sewer. 
/=  thickness  of  brick  work  in  feet. 
Rankine's   Rule.— 


£=  thickness  in  feet. 
r~=.  internal  radius  in  feet. 
c=  0.2  for  concrete. 
0.3  for  block  stone. 
0.4  for  brick. 
0.45  for  rubble. 

Reinforcement  for  Sewers. — If  one  set  of  reinforcement  is 
used,  y*  per  cent  of  the  shell  area  usually  is  sufficient.  If  two 
sets  of  reinforcement  are  used,  one  at  intrado  and  one  at 
extrado,  y\  per  cent  is  usually  employed.  For  circular  pipes 
the  thickness  for  constructive  reasons  usually  is  made  con- 
stant. For  longitudinal  or  distributing  rods  the  author  uses 
one-half  the  area  of  carrying  rods,  spacing  them  50  per 
cent  further  apart.  If  the  annular  or  carrying  rods  are 
separate,  they  are  spliced  by  lapping  or  hooking.  In  either 


338 


REINFORCED    CONCRETE. 


case  all  rods  should  have  hooked  ends.  If  the  reinforcement 
is  spiral,  the  ends  of  the  helices  are  hooked,  overlapping 
40  diameters  and  tied  together  by  means  of  No.  1.8  an- 
nealed wire. 

The  carrying  and  distributing  rods  are  likewise  tied  to- 
gether at  crossings,  so  as  to  keep  them  stiff  and  in  their 
proper  position  during  concreting. 

In  most  instances  a  fabric  will  be  found  most  economical 
for  conduit  reinforcement. 

In  many  instances  one  or  two  layers  of  fabric  are  suffi- 
cient; if  not,  l/2  in.  or  ^  in.  steel  rods  are  tied  to  the  fabric 
where  required. 

A  conduit  located  in  an  arch  fill  is  stressed  according  to 
the  line  of  a  parabola  and  if  built  according  to  this  line  can 
be  of  remarkably  light  dimensions  and  still  withstand  a  very 
heavy  uniform  load. 

Such  conduits  must  of  course  be  carefully  back  filled,  but 
after  filling  there  is  little  danger  of  damaging  them. 

Thickness  and  Weight  of  Reinforced  Concrete  Pipe.— 
Table  LXXI  gives  a  list  of  light  weight  reinforced  concrete 
sewer  pipe  as  manufactured  in  Germany  and  Austria. 

TABLE  LXXI. — THICKNESS  AND  WEIGHT  OF  CONCRETE  PIPE. 


Circular  pipe. 

Egg-shaped  pipe. 

Diam.  in 
inches. 

Thickness 
inches. 

Wt.  per  lin. 
ft.  in  Ibs. 

Diam.  in 
inches. 

Thickness 
inches. 

Wt.  per  lin. 
ft.  in  Ibs. 

4 

91 

7x11 

1 

23 

6 

111 

10x15 

{ 

33 

8 

17 

12x18 

46 

10 

24 

14x21 

52 

12 

30 

16x24 

67 

14 

37 

20x30 

| 

87 

16 

j 

44 

22x33 

I 

105 

18 

1 

50 

24x36 

I 

110 

20 

22 

!i 

60 
67 

25x37i 
28x42 

120 

127 

27 

\\ 

100 

29x43 

1 

140 

33 

n 

146 

31x47 

ii 

173 

43 

if 

224 

40x60 

2 

266 

55 

2i 

335 

51x80 

21 

366 

63 

2i 

426 

75 

3 

580 

CULVERTS,  CONDUITS,  SEWERS,  DAMS. 


339 


TABLE  LXXI-A. 

Thickness  and  weight  of  reinforcement  in  culvert  and  sewer  pipe,  used  by  the  author. 
( NOTE.— These  culverts  are  furnished  by  Kansas  City  Concrete  Pipe  Co.,  Kansas  City,  Mo.; 


Diameter. 

Thickness. 

A.  S.  &  W.  Co.  Triangular  Mesh 
Wire  Reinforcing. 
Weight  per  sq.  ft. 

Draw  Bars. 

Number 

24  inches 

3     inches 

6  (Single) 

.271bs. 

l/i  inch  roun 

27 

3}/£      " 

6 

.27 

y%  ' 

30 

3/^2      " 

27 

.41 

y%  ' 

33 

4 

26 

.50 

y%  ' 

36 

4 

26 

.50 

y%  ' 

39 

4         || 

26 

.50 

y%  ' 

42 

26 

.50 

y%  * 

45 

4/^      " 

26 

.50 

y%  ' 

48 

5          " 

23 

.72 

y%  ' 

54 

5/^      "         • 

23 

.72 

y%  ' 

60 

6         " 

23 

.72 

y%  " 

66 

6^2        " 

23 

.72 

yi 

72 

7         " 

26  (Do 

able) 

.50ea 

ch 

¥  «• 

78 

7/^      " 

25 

.55 

84 

8 

23 

.72 

K2     " 

These  pipes  come  in  4-foot  lengths,  complete  with  locking  pins. 

Stresses  in  Pipes  and  Rings  According  to  Talbot's  Re- 
searches.— Prof.  A.  N.  Talbot  gives  the  following  data  in  his 
paper  on  results  of  tests  of  cast  iron  and  concrete  pipes  (Bul- 
letin No.  22,  University  of  Illinois  Experiment  Station, 
Urbana,  111.,  April  29,  1908) : 

Concentrated  Load. — For  a  concentrated  load,  Q  applied 
at  the  crown  of  a  ring,  the  bending  moment  Mb  for  a  pipe  of 
mean  external  diameter  D  is 

MB  =  0.159  QD. 
The  resisting  moment  is 

MR  =  \fcf> 

where  fc  =  unit  stress  at  the  most  remote  fiber 
t  =  thickness  of  the  ring. 


340 


REINFORCED    CONCRETE. 


Distributed    Vertical    Load. — For    a    distributed    vertical 
load  on  thin  elastic  ring,  the  determination  of  the  values  of  M 
and  MB  is  given  as  follows  (see  Fig.  137) : 

If  a  system  of  horizontal  forces  equal  to 
the  vertical  forces  here  considered  be  ap- 
plied to  a  ring,  the  bending  moment  pro- 
duced at  A  by  the  horizontal  forces  will  be 
the  same  as  that  produced  at  B  with  the 
vertical  load,  and  the  bending  moment  pro- 
duced at  B  will  be  the  same  as  that  found 
at  A  with  a  vertical  load,  but  with  opposite 
signs  in  each  case. 

Similarly,  at  any  point  between  A  and  B 
it  is  evident  that  an  equal  numerical  bend- 
ing moment  will  be  produced  with  the  new  loading  as  at  corre- 
sponding points  with  the  old  loading,  but  with  opposite  signs. 
The  effect  of  a  combination  of  the  vertical  and  horizontal  loads 
will  be  the  same  as  that  of  a  load  normal  to  every  part  of  the 
ring  and  making  the  bending  moment  at  every  section  zero. 
It  follows  then  that 

WD 


J 


Fig.   137. 


M 


16 


where  W  =  the  total  distributed  load  on  a  ring  of  unit  length, 
and  D  the  mean  diameter  of  the  ring. 

Taking  0  —  45°  the  bending  moment  above  this  point  of  the 
ring  is  positive,  below  it  is  negative. 

Distributed  Vertical  and  Horizontal  Load. — In  thin  elastic 
ring  it  is  found  that 


wr* 


(56) 


where 

2r  =  average  diameter  of  ring. 

q  =  the  ratio  of  the  horizontal  to  the  vertical  pressure. 

The  bending  moment  becomes  zero  at  0  =  45°,  as  in  the 
Other  case. 


CULVERTS,  CONDUITS,  SEWERS,  DAMS.          341 

If  the  horizontal  pressure  has  the  same  value  as  the  vertical 
pressure,  q  =•  1  and  M  becomes  zero  at  all  points.  This  corre- 
sponds to  a  uniform  external  pressure  and  produces  equal  com- 
pression in  all  parts  of  the  ring. 

Thus  for  a  concentrated  load  we  have  for  the  most  remote 
fiber 


(57) 

At  any  point  of  the  ring  forming  an  angle    0  with  the  hori- 
zontal, we  have: 


For  a  uniformly  distributed  horizontal  load  the  stress  at  the 
crown  B  will  be 

WD 

/=  I1*  -pr  .....................  :  ..........  (59) 

•At/4, 

W          WD 
f=%--l-t-  .....................  .  .....  ,  (60) 

and  at  any  given  point, 

wr  cos2  0        M 


f  =  --  Y~  "  -  J7» 


For  a  distributed  horizontal  and  vertical  load,  we  have  at 
the  crown  B, 

qwr         Ac  WD 

f^^r*-^  .........................  (62) 

At  A,  the  extremity  of  the  horizontal  diameter, 

wr         J«  WD 
1-~t~^~    .>•  ..................  ......    (63) 

and  at  any  given  point, 

wr  cos2  0         <mr  sin2  0         M 

f--^-         -r--±p-8----  .........  (64) 

These  conditions  are  not  strictly  true  for  reinforced  concrete. 

As  the  amount  of  reinforcement  is  usually  lower  than  that  in 
which  the  circular  beam  would  fail  by  compression  in  the  con- 
crete, we  may  take  for  the  resisting  moment  of  the  reinforced 
concrete  section 


342  REINFORCED    CONCRETE. 

MR  =  0.87  Asfd  ................  (65) 

where  Aa  is  area  of  cross  section  of  reinforcement  for  unit  length 
of  ring. 

d  =  distance  from  compression  face  to  center  of  steel  rein- 
forcement. 

/  —  tensile  stress  in  steel  due  to  bending  moment. 

The  actual  tensile  stress  in  the  steel  at  A,  the  extremity  of 
the  horizontal  diameter,  is 


being  reduced  by  the  resisting  compressive  stresses. 

Here  /  is  calculated  by  equating  0.87  A  sfd  to  the  bending 
moment  at  the  section  considered. 

p  =  ratio  of  area  of  reinforcement  for  a  unit  length  of  beam 
or  ring  to  the  distance  between  the  center  of  the  steel  and  the 
compression  face  of  the  concrete. 

T  —  the  thrust  or  pressure  against  the  face  of  the  section 
and 

n  =  the  ratio  of  the  moduli  of  elasticity,  which  for  this  pur- 
pose may  be  taken  as  15.  At  the  extremity  of  the  horizontal 
diameter, 

T=y   ...................    (67) 

and  at  the  crown  it  is  zero  for  vertical  loading,  and  for  both 
concentrated  and  distributed  load  the  greatest  tensile  stress  is 
found  in  this  section. 

Summary  of  Tests  Made  on  Concrete  Pipes,*—  (1)  The 
reinforced  concrete  rings  in  the  concentrated  load  test  held  their 
maximum  loads  through  a  considerable  deflection,  thus  showing 
a  quality  which  is  of  value  when  changes  in  earth  conditions 
permit  a  gradual  yielding  of  the  surrounding  earth.  The  cal- 
culated restraining  moment  agrees  fairly  well  with  the  calcu- 
lated bending  moment. 

(2)  The  reinforced  concrete  rings  and  pipes  tested  under 
distributed  load  made  a  satisfactory  showing.  The  so-called 
critical  failure  may  occur  by  either  tension  failure  in  the  steel 

*Prof.  A.  N.  Talbot,  Bulletin  No.  22,  University  of  111.,  Urbana,  111. 


CULVERTS,  CONDUITS,  SEWERS,  DAMS.          343 

or  a  diagonal  tension  failure  (ordinarily  called  shearing  fail- 
ure) in  the  concrete.  A  flattened  arc  for  the  reinforcement 
where  it  approaches  the  "inner  face  is  of  assistance,  and  stirrups 
may  be  of  some  value.  Beyond  the  critical  load  the  reinforce- 
ment is  of  service  in  distributing  the  cracks  and  in  holding  the 
concrete  together.  Final  failure  is  by  crushing  of  the  concrete 
in  much  the  same  way  as  was  obtained  with  plain  concrete 
rings.  The  additional  strength  beyond  the  critical  load  may  be 
taken  into  consideration  in  selecting  the  factor  of  safety  or 
working  strength. 

(3)  The  restraint  of  the  sand  in  the  test  is  very  important 
and  the  effect  is  to  reduce  the  bending  moment  developed  by  a 
given  vertical  load  or,  as  it  would  be  commonly  stated,  to  add 
strength  to  the  pipe.  The  degree  of  permanency  of  this  side 
restraint  is  uncertain.  It  seems  evident  in  these  tests  that  the 
distribution  of  the  pressure,  both  horizontal  and  vertical,  was 
not  uniform,  and  that  with  the  usual  method  of  placing  a  pipe 
in  an  embankment  and  especially  when  other  materials  than  sand 
are  used,  the  distribution  would  be  even  less  uniform  than  here 
found. 

In  view  of  this  it  will  be  well  in  making  calculations  and  de- 
signs to  use  the  formula 


- 
•  ~     16 

for  the  bending  moment,  thus  considering  that  the  side  of  re- 
straint is  offset  by  the  uneven  distribution  of  the  load,  any  sur- 
plus from  this  being  considered  merely  as  additional  margin  of 
safety. 

For  pipes  poorly  bedded  and  filled,  a  larger  bending  moment 

WD 

than    1g    should  be  used. 
lo 

(4)  The  method  of  bedding  and  laying  pipes,  the  nature  of 
the  bed  and  the  surrounding  earth  have  a  great  effect  upon  the 
bending  moment  developed  and  upon  the  resistance  of  the  pipe 
to  failure. 

If  the  greatest  supported  pressure  comes  at  points  well  to 
the  side  of  the  bottom  element,  as  may  be  obtained  by  careful 


344 


REINFORCED    CONCRETE. 


bedding,  the  bending  moment  is  reduced.  It  is  also  plain  that 
the  bell  should  be  left  free  from  pressure  at  the  bottom.  It  is 
possible  that  the  presence  of  a  bell  detracts  from  the  strength 
of  a  pipe.  Any  action  in  filling  which  increases  the  lateral  re- 
straint against  the  pipe  will  add  to  the  security  of  the  struc- 
ture. 

Forms  for  Sewers. — Forms  for  sewers  are  either  of  wood 
or  metal,  the  patented  forms  being  of  metal.  Fig.  138  shows  a 
center  for  an  8-ft.  conduit  used  in  the  Pittsburg  filtration  sys- 


i          ^E3Bm_JjU--«sCy~          I    :     V    1 

^^aEip^^i  l&f  l"^*- 


Fig.  138.— Center  for  8-Ft.  Conduit, 
Pittsburg  Filtration   System. 


Fig.    139.— Blaw   Collapsible 

Steel  Centering  for 

Sewers. 


tern,  so  arranged  that  it  can  be  easily  taken  apart,  only  bolts 
being  used  to  assemble  the  form. 

Fig.  139  shows  a  collapsible  steel  center  patented  by  the  Blaw 
Collapsible  Steel  Centering  Co.,  Pittsburg.  The  operation  of 
this  centering  is  self  explanatory. 

Fig.  140  shows  the  method  of  using  metal  lagging  for  the 
form  of  a  13%-ft.  sewer,  as  patented  by  the  Duralite  Co.,  New 
York  City.  The  lagging  consists  of  two  plain  sheets  of  metal 
rigidly  attached  to  an  intermediate  corrugated  metal  sheet.  Fig. 
140  shows  the  form  for  a  sewer  built  to  receive  later  a  4-in. 


CULVERTS,  CONDUITS,  SEWERS,  DAMS. 


345 


brick  invert  lining.  In  constructing  this  lagging  for  arch  forms 
the  outside  steel  sheet  away  from  the  concrete  is  replaced  by 
narrow  strips  or  bands  which  are  bolted  to  the  flat  outside  parts 
of  the  corrugated  sheet.  The  spacing  of  the  bolt  holes  in  the 
bands  determines  the  radius  of  the  panel.  One  of  the  best  adapt- 
tions  of  this  form  is  in  molds  for  sewers,  conduits,  etc.,  where 
it  may  be  entirely  self-supporting  and  does  not  require  any  in- 
side bracing  or  studding.  This  obviates  the  adjustment  of  any 


Fig.    140.— Metal   Lagging   for  Form  for  13% -Ft.    Sewer. 

moving  parts  in  collapsing  and  moving  forward,  and  leaves  al- 
most the  entire  cross-section  of  the  bore  clear  for  the  workmen 
or  for  the  operation  of  material  cars  in  tunnel  work.  It  has 
the  added  advantage  that  rear  sections  of  the  centering  on  which 
the  masonry  has  taken  its  set  can  be  collapsed,  drawn  through 
the  forward  sections  where  the  masonry  is  being  laid  and  set 
up  in  advance.  This  feature  effects  an  economy  of  some  20 
per  cent  to  40  per  cent  in  the  total  feet  of  centering  required 


346 


REINFORCED    CONCRETE. 


Oepfh  of  Trench  in  Feet 

2     4      6     &     10    12     14    16    IS    ZO  ZZ 


Fig.  140-A. — Average  Bids  on  Pipe  Sewers. 
SEWER  BIDS  IN  THE  CENTRAL  STATES. 
The   Riggs   &  Sherman   Co.,   of  Toledo,   Ohio,  have  pre- 
pared from  schedules  of  100  bids  received  for  pipe  sewers  in 
1908  on  its  work  in  Ohio,  Indiana  and  Michigan  the  accom- 
panying diagram  of  the  average  of  all  these  tenders.     The 
upper  curve  is  for  furnishing  and  laying  pipe,  while  the  lower 
curves  are  for  trenching,  furnishing  and  laying. 


CULVERTS,  CONDUITS,  SEWERS,  DAMS. 


347 


on  continuous  work.  It  also  makes  possible,  where  desired,  ab- 
solute monolithic  construction  without  vertical  or  horizontal 
joints. 

DAMS. 

Classification. — Dams  are  of  two  classes,  (1)  gravity  or 
solid  dams,  where  the  water  pressure  tends  to  slide,  rupture  or 
overturn  the  dam,  and  (2)  pressure  dams  or  inclined  dams, 
where  the  water  pressure  acts  with  the  weight  of  the  structure 
to  assist  its  stability. 


Full 


Fig.  141. — Forces  Acting  on  a  Solid  Dam. 

Comparative  Features. — The  method  herein  outlined  for 
showing  the  comparative  stresses  in  solid  and  pressure  dams  is 
the  one  used  by  the  Ambursen  Hydraulic  Construction  Co.,  Bos- 
ton. In  Fig.  141,  which  shows  a  solid  dam,  the  water  pressure  is 
represented  in  intensity  and  direction  by  the  line  PC  for  a  full 
dam  and  P\C\  for  a  10- ft.  overflow.  The  overturning  momenta 
about  the  toe  T  are,  respectively: 

M  =  P  C   X  p  T  and 

Ml=PlCl  xpiT 


348 


REINFORCED    CONCRETE. 


showing  that  both  pressure   and  leverage   are   increased  by  in- 
creased   overflow.      The  moment  of   resistance   MR   in   either 
case  is  the  weight  of  the  dam  W  multiplied  by  the  distance  from 
toe  to  perpendicular  through  center  of  gravity. 
The  factor  of  safety  is, 

M        MI 


as  the  case  may  be,  and  decreases  rapidly  as  the  water  rises. 
Owing  to  the  great  cost  of  solid  dams,  this  factor  of  safety  is 
usually  cut  down  to  about  2.5. 

'We,  10  ft.  Flood 


Ws   Full 


Fig.    142.— Resultants   of  Forces   Acting  on  a   Solid  Dam. 

The  normal  section  of  a  reinforced  concrete  dam  is  trian- 
gular and  thereby  becomes  a  pressure  dam,  showing  a  far  greater 
factor  of  safety,  which  increases  with  the  depth  of  water. 

Fig.  142  is  the  ordinary  section  of  a  solid  dam.  Its  normal 
design  is  sucn  that  when  empty  the  line  of  pressure  cuts  the  up- 


CULVERTS,  CONDUITS,  SEWERS,  DAMS. 


349 


stream  edge  of  the  middle  third  at  Ri.  As  the  dam  fills  up  the 
resultants  of  the  water  pressure  and  the  weight  of  the  dam  ad- 
vance steadily  and  with  increasing  inclination  down  stream  to- 
ward the  toe,  until  when  the  calculated  flood  height  is  reached 
the  resultant  cuts  the  down  stream  edge  of  the  middle  third  at 
Ro.  Under  these  conditions  the  distribution  of  pressure  on  the 
base  is  represented  by  the  triangle  B  T  D,  there  being  no  press- 
ure at  all  at  the  heel  and  a  maximum  pressure  at  the  toe.  Now. 
if  some  extraordinary  flood  happens,  the  resultant  will  advance 
to  A  A,  the  distribution  of  pressures  will  be  on  O  N  T,  the 


Fig.    143. — Resultants    of  Forces  Acting   on   a   Reinforced   Concrete 

Dam. 


virtual  base  of  the  dam  will  be  reduced  to  M  T,  the  dam  will 
lift  at  the  heel  and  the  pressure  at  the  toe  of  the  dam  will  ex- 
ceed the  safe  limit.  So  at  a  certain  point  the  dam  ruptures  or 
is  seriously  weakened.  By  no  chance,  under  working  conditions, 
is  the  pressure  ever  where  it  ought  to  be  namely,  on  the  center 
of  the  base  to  give  an  equal  distribution. 

On  the  other  hand,  a  dam  having  a  triangular  section  behaves 
in  an  entirely  different  manner.     Thus  in  Fig.  143  the  pressure 


350  REINFORCED    CONCRETE. 

resultant  when  empty  is  exactly  at  the  center  of  the  base.  A? 
the  pond  fills  the  resultants  move  up  stream  instead  of  down 
stream  through  the  successive  positions  Rn  and  R3  until  with  the 
dam  three-quarters  full  the  resultant  reaches  the  extreme  posi- 
tion of  Ri,  but  even  then  not  approaching  the  limit  of  the  mid- 
dle third.  When  the  dam  is  full  the  resultant  moves  back  to- 
wards the  center  to  position  Rs,  and  under  maximum  flood  it  as- 
sumes the  position  Ro,  having  returned  nearly  to  the  center. 
Under  these  conditions  the  base  pressures  are  shown  by  the 
shaded  trapezoid  and  are  very  nearly  uniform  in  distribution. 
The  excess  of  pressure  is  purposely  thrown  toward  the  heel  of 
the  dam  where  it  receives  the  additional  support  of  the  cutoff 
wall. 

The  effect  of  the  weight  of  the  water  flowing  down  the  apron 
is  not  easy  to  calculate,  but  it  is  certain  that  it  straightens  up  the 
resultant  and  moves  it  still  nearer  the  center  of  the  dam.  Under 
maximum  flood  the  pressure  is  substantially  at  the  center  of  the 
dam  and  the  distribution  over  the  base  is  practically  uniform. 
Hence,  extraordinary  floods,  instead  of  increasing  the  risk  to  .the 
dam,  actually  decrease  it  by  forcing  the  resultant  still  nearer 
the  center. 

Pressure  on  the  Immersed  Surface.* — The  usual  method 
of  finding  the  pressure  on  the  immersed  surface  of  a  dam,  the 
overturning  moment  and  the  resultant  on  the  base,  is  illustrated 
in  Fig.  144. 

Let  BC  be  the  immersed  surface,  DC  the  base,  BT  the  sur- 
face of  the  water,  and  x  the  depth  of  the  water.  Draw  CK  per- 
pendicular to  BC  and  equal  to  x;  then  will  the  weight  of  the 
water  in.  the  prism  BCK,  of  a  length  unity,  be  the  amount  of 
the  pressure  on  the  immersed  surface  one  unit  in  length.  This 
pressure  P  will  act  normal  to  the  surface  BC  and  through  the 
center  of  gravity  of  the  triangle  BCK  at  G  and  will  intersect  BC 
at  M,  CM  being  equal  to  one-third  of  BC. 

Find  the  center  of  gravity  of  the  section  of  the  dam  DABC 
and  its  weight  W.  From  the  intersection  of  P  with  the  vertical 

*Buel  and  Hill,  "Reinforced  Concrete." 


CULVERTS,  CONDUITS,  SEWERS,  DAMS. 


351 


through  the  center  of  gravity  of  the  dam  at  N  lay  off  NO  equal 
to  the  weight  W  by  the  scale  of  forces,  and  draw  OS  parallel 
to  NG,  making  OS  equal  to  P  by  the  scale  of  forces.  Then  the 
resultant  on  the  base  R  will  •  be  represented  in  direction  and 
amount  by  the  line  SN,  and  its  intersection  with  the  base  at  q  will 
be  the  center  of  reactions  on  the  base.  If  q  is  found  within  the 
middle  third  of  the  base  the  dam  will  be  in  stable  equilibrium, 
provided  the  maximum  intensity  of  pressure  on  the  foundation 
is  not  excessive.  The  intensity  of  pressure  on  any  part  of  the 
base  may  be  found  by  the  method  given  for  retaining  walls,  using 
the  vertical  component  of  R  acting  through  q. 


Fig.   144. — Graphical   Solution  of  the  Forces  Acting  on  a  Dam. 

When  the  immersed  surface  is  vertical  the  methods  given  for 
finding  the  thrust  on  retaining  walls  are  applicable  by  making 
0  equal  to  zero. 

When  the  crest  is  submerged  the  solution  will  be  as  follows : 
Produce  the  line  BC  to  intersect  the  surface  of  the  water  at  E 
and  lay  off  CK'  equal  to  x'  and  perpendicular  to  EEC.  Draw 


352  REINFORCED    CONCRETE. 

BK"  perpendicular  to  BC  from  the  crest  and  find  the  center  of 
gravity  of  of  BK"K'C.  This  may  be  done  by  locating  the  centers 
of  gravity  of  the  triangles  ECK',  BCK  and  EBK"  at  g,  G  and  g 
respectively,  and  that  of  the  parallelogram  BKK'K"  by  the  in- 
tersection of  the  diagonals  at  I,  then  the  center  of  gravity  of 
BK"K'C  will  be  at  G'  where  gl  intersects  g'g  produced.  The 
area  of  BK"K'C  is  the  difference  of  the  areas  of  the  triangles 
ECK'  and  EBK". 

A  force  equal  to  the  weight  of  BCK'K",  for  a  length  unity, 
acting  through  G'  normal  to  BC  at  M'  will  be  the  resultant 
pressure  P'  on  a  unit  length  of  the  surface  BC. 

Find  the  weight  W  of  a  unit  of  length  of  the  section  of  the 
dam  and  the  pressure  of  water  AEFB,  over  the  crest,  and  the 
intersection  of  the  vertical  through  the  common  center  of  grav- 
ity with  P'  at  N',  and  lay  off  N'O'  vertical  and  equal  to  W. 

Draw  O'S'  parallel  and  equal  to  P',  then  S'N'  will  be  the  re- 
sultant Rf,  intersecting  the  base  at  q[.  The  values  of  P,  W,  R 
and  the  distance  DQ' ,  given  in  Fig.  144,  were  found  by  assuming 
the  following: 

*  =  15  ft. 

*'  =  20  ft. 

DC  =  15  ft. 

The  batter  of  AD  =  3  ft.  in  its  height. 

The  crest  AB  —  3  ft. 

The  average  weight  of  the  prism  of  the  dam  =  140  Ibs.  per 
cu.  ft.,  and  the  weight  of  water  =  62.5  Ibs.  per  cu.  ft. 

For  P,  W,  R  and  DQ  the  water  level  is  at  ABT,  and  for  P', 
W,  R',  and  DQ'  the  surface  of  the  water  is  at  EFT. 

Conclusion. — Dams  are  either  designed  as  thin  slabs  sup- 
ported on  beams  between  counterforts,  spacing  the  beams  closer 
at  the  bottom  and  spreading  them  towards  the  top— or  in  the 
shape  of  a  floor  slab  varying  in  thickness  from  bottom  towards 
the  top  according  to  the  water  pressure. 

Owing  to  the  lighter  weight  of  reinforced  concrete  dams, 
provision  must  be  made  to  prevent  them  from  sliding.  This  is 


CULVERTS,  CONDUITS,  SEWERS,  DAMS. 


353 


The  following  table  gives  the  intensity  of  the  horizontal 
pressure,  />,  at  any  depth,  h,  the  total  pressure  H,  above  the 
section  considered,  and  the  overturning  moment,  M,  in  inch 
Ibs.,  at  the  section  A-B :  ("Designing  Methods") 


FLUID  PRESSURE. 
a/=62.5  Ibs. 


Fig.  144-A. 
TABLE  LXXI-A. 


h 

t>=wh 

H= 

Yrth 

Overturning 
Moment 
M=±Hh 

* 

t>=wh 

H= 

Yrth 

Overturning 
Moment 
M=±Hh 

Feet. 

Pounds. 

Pounds. 

Inch  Pounds. 

Feet. 

Pounds. 

Pounds. 

Inch  Pounds. 

1 

62.5 

31 

124 

16 

1000.0 

8000 

512000 

2 

125.0 

125 

1000 

17 

1062.5 

9031 

614108 

3 

187.5 

281 

3372 

18 

1125.0 

10125 

729000 

4 

250.0 

500 

8000 

19 

1187.5 

11281 

857366 

5 

312.5 

781 

15620 

20 

1250.0 

12500 

1000000 

6 

375.0 

1125 

27000 

21 

1312  5 

13781 

1157604 

7 

437.5 

1531 

42868 

22 

1375.0 

15125 

1331000 

8 

500.0 

2000 

64000 

23 

1437.5 

16531 

1520852 

9 

562.5 

2531 

91116 

24 

1500.0 

18000 

1728000 

10 

625.0 

3125 

125000 

25 

1562.5 

19531 

1953100 

11 

687.5 

3781 

166364 

26 

1625.0 

21125 

2197000 

12 

750.0 

4500 

216000 

27 

1687.5 

22781 

2460348 

13 

812.5 

5281 

274612 

28 

,1750.0 

24500 

2744000 

14 

875.0 

6125 

343000 

29 

1812.5 

262811 

3048596 

15 

937.5 

7031 

421860 

30 

1875.0 

28125 

3375000 

354 


REINFORCED    CONCRETE. 


done  by  anchoring  or  filling  the  hollow  space  with  sand  and 
gravel  or  lean  concrete. 

Computing  the  dimensions  of  slabs,  beams  or  counterforts  is 
very  simple  after  the  pressures  have  been  determined,  and  is 
done  according  to  the  methods  laid  down  for  floors  and  girders 
of  buildings. 

Types  of  Construction. — There  are  three  principal  types 
of  construction — the  open  front  dam,  the  half  apron  dam  and 
the  curtain  dam. 


cite* 


Fig.    145.— Reinforced  Concrete  Dam,    Theresa,  N.   Y. 

The  Open  Front  Dam. — An  example  of  this  type  of  dam 
is  the  one  built  at  Theresa,  N.  Y.,  shown  in  Fig.  145.  This  dam 
is  built  of  concrete  reinforced  with  Thacher  rods  and  expanded 
metal;  it  is  120  ft.  long  and  11  ft.  high  and  is  founded  on  solid 
rock.  The  structure  consists  of  a  series  of  solid  concrete  but- 
tresses 12  ins.  thick  and  spaced  6  ft.  apart  center  to  center,  and 
of  a  reinforced  plate  supported  on  the  inclined  tops  of  the  but- 
tresses. At  the  crest  the  plate  is  stiffened  by  a  reinforced  beam 
6x8  ins.  in  section.  The  plate  was  made  of  concrete  composed 
of  1  part  Portland  cement,  2  parts  sand,  and  4  parts  broken  lime- 
stone; the  toe  and  buttresses  were  made  of  a  1-3-6  mixture. 
The  buttresses  were  anchor-bolted  to  the  rock  by  3-ft.  1^4-in. 
bolts.  The  drawing  shows  the  spacing  of  the  rods  and  their  di- 


CULVERTS,  CONDUITS,  SEWERS,  DAMS. 


355 


mensions.  The  dam  is  so  constructed  that  the  resultant  pressure 
falls  always  within  the  base,  and  it  is  therefore  a  gravity  dam  un- 
der all  heads  of  water.  About  125  cu.  yds.  of  concrete  were  re- 
quired to  construct  the  dam.  It  was  constructed  by  the  Ambur- 
sen  Hydraulic  Construction  Co.,  Boston.  The  open  front  type 
is  used  for  moderate  heights,  and  when  located  on  a  ledge  of 
hard  rock  is  able  to  withstand  the  erosion  from  the  overflow  of 
water  and  ice. 

The  Half  Apron  Dam. — This  type  is  a  modification  of  the 
former  and  consists  in  carrying  the  apron  down  in  front  to  with  • 
in  6  or  8  ft.  of  the  bottom,  so  curved  as  to  discharge  the  water 
with  a  high  velocity  in  a  horizontal  direction,  as  shown  in 
Fig.  146. 


^  Roll  way 


\Rbck  Line  ^ 
Fig.    146. — Half   Apron    Type   of  Dam. 

The  Curtain  Dam. — This  type  goes  still  further  and  con- 
tinues the  apron  to  the  river  bed,  entirely  enclosing  the  interior, 
as  illustrated  in  Fig.  147.  It  is  customary  to  place  vents  in 
the  apron  just  below  the  crest  for  the  purpose  of  admitting  air 
behind  the  sheet  of  water  to  destroy  the  partial  vacuum  which 
would  otherwise  form  under  high  velocities  of  overflow  during 
floods — and  which  is  the  cause  of  the  so-called  trembling  of 
dams. 


356 


REINFORCED    CONCRETE. 


Where  foundations  are  on  hard  clay  or  cemented  sand,  sheet 
piling  is  often  driven  at  the  heel  and  toe  to  a  sufficient  depth 
to  insure  tightness,  and  the  concrete  is  placed  over  and  about 
the  head  of  the  piling.  Drain  holes  are  placed  in  the  toe  to 


Fig.   147.— Curtain   Type  of  Dam. 

carry  off  seepage.  Weep  holes  may  be  placed  in  the  floor  to  pre- 
vent upward  pressure  on  the  floor,  which  might  endanger  the 
safety  of  the  dam. 


CHAPTER  VI. 

TANKS,  RESERVOIRS,  BINS  AND  GRAIN  ELEVATORS. 
TANKS  AND  RESERVOIRS. 

General  Discussion. — The  construction  of  tanks  and  reser- 
voirs in  reinforced  concrete  is  like  pipes,  in  that  it  is  one  of 
the  first  applications  of  this  material  in  building  construction. 
Monier  constructed  a  42,000-gallon  tank  at  Maisons-Alfort  in 
1868  and  another  of  23,000  gallons'  capacity  at  Bougival  in  1872 
for  the  local  water  works.  The  number  of  reinforced  concrete 
tanks  already  in  existence  is  a  proof  of  their  fast  increasing 
popularity. 

Reinforced  concrete  is  not  only  suitable  and  adapted  for  wa- 
ter storage,  but  likewise  for  wines,  vinegar,  petroleum,  oil,  and 
solid  substances,  such  as  grain,  cement  in  bulk,  coal,  ore,  ashes, 
etc.  They  are  used  for  these  purposes  with  great  success  in  tan- 
neries, distilleries,  sugar  refineries,  breweries,  paper  mills,  bleach- 
cries,  and  other  places  where  reservoirs  are  wanted  for  any  pur- 
pose. Their  cheapness,  remarkable  lightness  and  elasticity 
cause  great  reduction  in  the  size  and  character  of  supports  and 
foundations,  and  the  minimum  cost  of  maintenance  and  atten- 
tion required  has  recommended  reinforced  concrete  as  an  ideal 
material  of  construction  for  these  various  purposes. 

Shape  or  Form  of  Tanks  and  Reservoirs. — For  covered 
tanks  the  roofs  assume  the  form  of  cones,  domes,  and  spheres, 
or  are  also  flat  and  calculated  accordingly.  The  shape  or  form 
of  the  reservoirs  may  be  round,  elliptical,  square,  or  polygonal, 
and  the  tanks  may  be  located  in,  on,  or  above  the  ground,  like- 
wise supported  on  columns,  walls,  or  girders,  as  the  case  may 
be.  The  cost  largely  depends  upon  the  form,  the  cylindrical 
tanks  being  the  more  simple  inasmuch  as  only  the  tension  from 

357 


358  REINFORCED   CONCRETE. 

the  interior  pressure  and  the  compression  due  to  the  weight  of 
the  walls  and  the  roof  must  be  considered,  while  in  the  rectan- 
gular or  hexagonal  structures  the  bending  moments  come  promi- 
nently into  consideration.  If  reservoirs  are  placed  on  the  ground 
and  subjected  to  compression  from  underneath,  the  spherical 
bottoms  are  concave  and  are  turned  downwards. 

Calculations.  —  The  calculations  for  circular  tanks  contain- 
ing liquids  are  very  simple. 

Let  T  =  tensile  stress  exerted  on  wall  for  1  foot  in  height  at 

a  depth  of  h  from  the  top. 
AB  =  area  of  steel  required  in  1  -ft.  of  height. 
d  =  diameter  of  tank  in  feet. 

w  =  weight  per  cu.  ft.  of  the  liquid  contained  in  the  tank. 
fs  =  unit  stress  in  the  reinforcement. 
h  =  depth  of  the  tank  at  a  point  where  the  thickness  is 

sought. 
Then 


(68) 

(69) 


Table  Giving  Capacity  of  Tanks.—  Table  LXXII  gives  the 
capacity  in  cubic  feet  and  gallons  for  each  1  ft.  depth  of  tanks 
of  different  diameters.  To  obtain  the  number  of  bushels  ca- 
pacity, multiply  the  number  of  cubic  feet  by  0.8.  For  example, 
a  tank  12  ft.  in  diameter  contains  113.10  cu.  ft.;  for  each  foot 
in  height  it  would  contain  113.10  X  0.8  =  90.48  bu. 

Foundations.  —  Tank  bottoms  may  rest  on  rock  or  hard- 
pan  and  need  be  only  of  sufficient  thickness  to  contain  the  re- 
inforcement and  insure  proper  connection  with  the  side  walls. 
On  soft  homogeneous  ground,  a  layer  of  common  concrete  placed 
under  the  bottom  is  usually  sufficient.  Where  the  soil  contains 
water  under  pressure,  very  careful  calculations  must  be  made 
to  enable  the  bottom  to  withstand  the  buoyancy  of  the  tank,  and 
in  these  cases  a  rib  or  gridiron  construction  is  often  resorted  to. 


TANKS,  BINS,  GRAIN  ELEVATORS. 


359 


TABLE  LXXII. — CAPACITY  OP  TANKS. 


5 

1 

ill 
I!? 

Diameter. 

i 

Gallons 
for  depth 
of  1  foot. 

Diameter. 

ll* 

1 

ft.  ins. 

ft.  ins. 

ft. 

1   0 

.785 

5.87 

5  0 

19.63 

146.88 

33 

855.30 

6398.1 

1 

.922 

6.89 

3 

21.65 

161.93 

34 

907.92 

6791.7 

2 

1.069 

8.00 

6 

23.76 

177.72 

35 

962.11 

7197.1 

3 

1.227 

9.18 

9 

25.97 

194.25 

36 

1017.88 

7614.3 

4 

1.396 

10.44 

6  0 

28.27 

211.51 

37 

1075.21 

8043.1 

5 

1.576 

11.79 

3 

30.68 

229.50 

38 

1134.11 

8483.8 

6 

1.767 

13.22 

6 

33.18 

248.23 

39 

1194.59 

8936.2 

7 

1.969 

14.73 

9 

35.78 

267.69 

40 

1256.64 

9400.5 

8 

2.182 

16.32 

7  0 

38.48 

287.88 

41 

1320.25 

9876.2 

9 

2.405 

17.99 

3 

41.28 

308.81 

42 

1385.44 

10363.9 

10 

2.640 

19.75 

6 

44.18 

330.48 

43 

1452.20 

10863.2 

11 

2.885 

21.58 

9 

47.17 

352.88 

44 

1520.53 

11374.4 

2   0 

3.142 

23.50 

8  0 

50.27 

376.01 

45 

1590.43 

11897.3 

1 

3.409 

25.50 

3 

53.46 

399.88 

46 

1661.90 

12431.9 

2 

3.687 

27.58 

6 

56.75 

424.48 

47 

1734.94 

12978.3 

3 

3.976 

29.74 

9 

60.13 

449.82 

48 

1809.56 

13536.5 

4 

4.276 

31.99 

9  0 

63.62 

475.89 

49 

1885.74 

14106.4 

5 

4.587 

34.31 

3 

67.20 

502.70 

50 

1963.50 

14688.0 

6 

4.909 

36.72 

6 

70.88 

530.24 

51 

2042.82 

15281.4 

7 

5.241 

39.21 

9 

74.66 

558.51 

52 

2123.72 

15886.5 

8 

5.585 

41.78 

10  0 

78.54 

587.52 

53 

2206.18 

16503.4 

9 

5.940 

44.43 

6 

86.59 

647.74 

54 

2290.22 

17132.1 

10 

6.305 

47.16 

11  0 

95.03 

710.90 

55 

2375.83 

17772.5 

11 

6.681 

49.98 

6 

103.87 

776.99 

56 

2463.01 

18424.6 

3  0 

7.069 

52.88 

12  0 

113.10 

846.0 

57 

2551.76 

19088.5 

1 

7.467 

55.86 

6 

122.72 

918.0 

58 

2642.08 

19764.2 

2 

7.876 

58.92 

13  0 

132.73 

992.9 

59 

2733.97 

20451.6 

3 

8.296 

62.06 

6 

143.14 

1070.8 

60 

2827.43 

21150.7 

4 

8.727 

65.28 

14  0 

153.94 

1151.5 

61 

2922.47 

21861.6 

5 

9.168 

68.58 

6 

165.13 

1235.3 

62 

3019.07 

22584.3 

6 

9.621 

71.97 

15  0 

176.71 

1321.9 

63 

3117.25 

23318.7 

7 

10.085 

75.44 

16  0 

201.06 

1504.1 

64 

3216.99 

24064.8 

8 

10.559 

78.99 

17  0 

226.98 

1697.9 

65 

3318.31 

24822.7 

9 

11.045 

82.62 

18  0 

254.47 

1903.6 

66 

3421.19 

25592.4 

10 

11.541 

86.33 

19  0 

283.53 

2120.9 

67 

3525.65 

26373.8 

11 

12.048 

90.13 

20  0 

314.16 

2350.1 

68 

3631.68 

27166.9 

4  0 

12.566 

94.00 

21 

346.36 

2591.0 

69 

3739.28 

27971  .8 

1 

13.095 

97.96 

22 

380.13 

2843.6 

70 

3848.45 

28788.5 

2 

13.635 

102.00 

23 

415.48 

3108.0 

71 

3959.19 

29616.9 

3 

14.186 

106.12 

24 

452.39 

3384.1 

72 

4071.50 

30457.0 

4 

14-748 

110.32 

25 

490.87 

3672.0 

73 

4185  39 

31308.9 

6 

15.321 

114.61 

26 

530.93 

3971.6 

74 

4300.84 

32172.6 

6 

15.904 

118.97 

27 

572.53 

4283.0 

75 

4417.86 

33048.0 

7 

16.498 

123.42 

28 

615.  Vo 

4606.2 

76 

4536.46 

33935.2 

8 

17.IC5 

127.95 

29 

660  .  52 

4941.0 

77 

4656.63 

34834.1 

9 

17.721 

132.56 

30 

706.86 

5287.7 

78 

4778.36 

35744.7 

10 

18.343 

137.25 

31 

754.77 

5646.1 

79 

4901.67 

36667.1 

11 

18.993 

142.02 

32 

804.25 

6016.2 

80 

5026.55 

37601.3 

*Also  area  of  circle  in  square  feet. 


360 


REINFORCED   CONCRETED 


Tightness  of  Tanks.— The  question  of  tightness  of  the 
tanks  is  of  the  greatest  importance  and  this  is  accomplished  in 
various  ways  by  different  constructors.  Often  a  tank  is  per- 
mitted to  leak  through  its  porous  parts  for  several  weeks,  after 
which  time  the  magnesia,  lime,  aluminum  salts  or  impurities  con- 
tained in  the  liquid  will,  to  a  great  extent,  close  up  the  pores 
by  silting.  The  author  has  found  that  the  best  method  of  making 
a  tank  tight  is  by  hard  troweling  on  the  inside  of  the  tank, 
such  plastering  being  done  before  the  final  setting  of  the  mortar 
or  concrete  of  which  the  tank  is  constructed.  The  author 


Fig.     148. — Reinforcement    for    Tanks. 

prefers  for  tanks  a  rather  dry  mixture  of  1  cement  to  4  coarse 
sand  well  tamped.  If  a  wet  mixture  is  used,  the  mortar  or  con- 
crete is  apt  to  contract  in  setting,  thereby  causing  initial  com- 
pressive  stresses  in  the  steel  reinforcement.  When  the  tank  is 
filled  the  concrete  will  crack  in  various  places  until  the  steel  re- 
ceives its  tension  stress.  This  is  the  common  cause  of  leaky 
tanks,  which  must  be  plastered  or  painted  afterwards. 

Reinforcement. — The   reinforcement   of   tanks   consists   of 
carrying  and  distributing  rods,  as  indicated  in  Fig.  148,  in  which 


TANKS,  BINS,  GRAIN  ELEVATORS.  361 

the  mesh  and  dimensions  are  proportioned  to  withstand  the 
pressure  and  tension  according  to  the  head  of  liquid  contained. 
The  reinforcement  is  usually  round  rods,  placed  annularly  round 
the  tank  either  in  separate  circles  or  in  helices,  such  reinforce- 
ment being  closer  together  and  stronger  nearer  the  bottom  of  the 
tank,  decreasing  in  area  towards  the  top.  The  distributing  rods 
are  usually  the  same  from  the  top  to  the  bottom  and  equal  to 
about  Vz  per  cent  of  the  area  of  the  tank  wall. 

For  square  tanks,  reinforcement  of  the  sides  by  brackets 
or  buttresses  usually  on  the  inside  becomes  necessary,  and  the 
walls  are  then  calculated  as  retaining  walls  supported  on  these 
brackets.  When  the  tanks  are  not  covered,  a  strong  rib  is 
usually  run  around  th£  top  construction,  similar  to  the  construc- 
tion used  in  open  steel  tanks  which  are  invariably  strengthened 
and  stiffened  by  riveting  an  angle  iron  around  the  top. 

Cost. — The  cost  of  reinforced  concrete  tanks  built  of  light 
dimensions,  but  of  rich  material,  resting  on  the  ground  and 
without  roof,  will  be  approximately  as  follows: 

For      1,000  gallons'  capacity 61A  cts.  per  gallon 

For     2,000  gallons'  capacity 5      cts.  per  gallon 

For     5,000  gallons'  capacity 4^  cts.  per  gallon 

For    10,000  gallons'  capacity 3%  cts.  per  gallon 

For   20,000  gallons'  capacity. 3      cts.  per  gallon 

For  100,000  gallons'  capacity 2      cts.  per  gallon 

For  200,000  gallons'  capacity 1%  cts.  per  gallon 

Tank  for  Montgomery  Ward  &  Co.,  Chicago  Heights,  111. 

—In  1901  the  author  constructed  a  40-ft.  tank,  8  ft.  deep,  for 
Montgomery  Ward  &  Co.,  Chicago  Heights.  The  tank  is  5  ft. 
underground  and  3  ft.  above  ground.  A  sump  1  ft.  in  diameter 
and  18  ins.  deep  was  put  at  a  point  near  the  circumference  and 
was  kept  empty  by  means  of  a  hand  pump,  the  water  being  con-^ 
veyed  away  for  a  distance  of  about  100  ft.  in  a  wooden  trough. 
The  walls  and  the  roof  are  only  2%  ins.  thick,  as  shown  in  Fig. 
149.  A  wire  fabric  of  No.  9  wire,  Ix6-in.  mesh,  was  erected 
near  the  center  of  the  wall,  and  reinforcing  rods  placed  on  the 
inside  of  the  netting  tied  at  the  side  by  means  of  annealed  wire. 


362 


REINFORCED    CONCRETE. 


The  soil  was  stiff  enough  to  stand  for  5  ft.,  so  that  no  form 
was  necessary  for  this  height.  The  bottom  being  3  ins.  thick,  it 
was  depressed  about  1  ft.  in  the  center  and  two  layers  of  net- 
ting were  laid  across  the  same  at  right  angles.  Around  the 
circumference  ^-in.  rods  3  ft.  long  were  hooked  at  both  ends, 
bent  to  a  right  angle  and  spaced  as  a  corner  angle  connection 


Fig.    149.— Roof  Plan   and   Section  of  Tank   for  Montgomery  Ward 

&    Co. 

every  12  ins.  The  bottom  was  plastered  with  a  mortar  of  1  part 
Portland  cement  to  3  parts  clean,  coarse  torpedo  sand.  The 
wire  mesh  around  the  sides  of  the  tank  was  steadied  by  means 
of  wooden  pegs  driven  into  the  earth.  The  plaster  on  the  sides 
commenced  at  the  bottom,  the  mortar  being  thrown  through  the 
mesh  against  the  earth  and  of  such  a  consistency  that  it  just  could 


TANKS,  BINS,  GRAIN  ELEVATORS. 


363 


be  retained  by  the  mesh.  A  few  minutes  later  a  second  man 
threw  on  the  next  coat  covering  the  mesh  and  the  rods  to  a 
depth  of  l/z  in.,  and  about  half  an  hour  later  followed  a  third 
man  with  a  third  coat  Vz  in.  thick.  After  this  coat  was  almost 
set  the  finisher  followed  up  with  a  1-2  mixture,  which  was  trow- 
eled smooth  with  an  iron  tool.  The  last  operation  gave  the 
tank  a  practically  glossy  surface  on  the  inside  similar  to  a  side- 
walk finish.  As  the  wooden  pegs  were  reached  they  were  pushed 


Fig.    150.— Detail    of    Connection    at    Roof     Tank    for    Montgomery 
Ward  &  Co. 

into  the  earth  and  new  pegs  put  in  near  the  top.  A  form  3  ft. 
high  made  of  %-in.  boards  nailed  to  2x6-in.  ribs  was  then  placed 
around  the  circumference  and  braced  back  on  the  ground  and 
the  plastering  operation  continued  until  the  entire  tank  was  plas- 
tered to  the  top,  which  took  four  plasterers  and  two  helpers  two 
days.  An  angle  iron  was  laid  around  the  top  of  the  tank  to  take 
the  thrust  of  the  roof,  and  anchored  by  running  the  ends  of  the 
wire  fabric  through  holes  punched  in  the  flange  of  the  angle 
iron,  as  shown  in  Fig.  150.  Then  a  conical  form  was  erected 


364 


REINFORCED    CONCRETE. 


^•Center  Post  Braced  from 

Outside  Scaffolding 

\ 

1 

1 

T 

§ 

\- 

^ 

ff^ 

,**• 

P  " 

6" 

1 
B 

f\ 

$    ^^^ 

:       j)                                                      --x^"^^^ 

i*-  Strap  Iron 

v5>^ 

*/na 

'Form 

/a 

H 

j-5' 

t    ' 

f 

^ 

9 

l~ 

f* 

£'0"Ben}-Rod5  1'0"C  toC 

%"xc_'0"F?ocfsJ'0"C1-oC      ^  A 

4 

j 

I 

f  I 

If 

^11        1 
te/^^ 

Bllfl  ^^  It         li 

j' 

T 

\ 

L— 

I" 
4'^"-  ^*- 

u    "_i-     "S1  '  ^ 

Fig.   151.— Section  of  Tank,  American  Steel  &   Wire  Co. 


TANKS,  BINS.  GRAIN  ELEVATORS.  365 

40  ft.  in  diameter  and  4  ft.  high  at  the  apex  to  support  the  roof, 
the  form  being  supported  on  studs  set  on  planks  laid  on  the 
bottom  of  the  tank.  The  form  consisted  of  2x6-in.  joists  and 
%-in.  sheathing  bent  down  on  the  radial  joists.  Wire  fabric 
was  laid  on  top  of  the  form  and  tied  to  radial  steel  rods,  which 
were  run  down  to  the  angle  iron  and  well  heeled.  An  expanded 


Fig.  152.— Plan  of  Fabric  in  Roof    Tank  for  American  Steel  &  Wire 

Company. 

metal  apron  was  thrown  over  the  angle  iron  and  fastened  to 
the  wire  netting  of  the  sides,  as  well  as  the  wire  netting  in  the 
roof,  so  as  to  form  a  clinch  for  the  mortar  around  the  top  cor- 
ner. In  Fig.  149  only  the  carrying  rods,  spaced  4  ins.,  are 
shown.  The  distributing  rods  of  the  fabric  are  spaced  1  in. 
apart.  The  roof  was  plastered  2%  ins.  thick  in  a  manner  simi- 


366 


REINFORCED    CONCRETE. 


lar  to  the  one  used  for  the  sides.  A  manhole  was  left  in  the 
roof  through  which  the  forms  were  taken  out.  The  sump  was 
made  tight  by  placing  a  nipple  18  ins.  long  with  a  flange  at  the 
lower  end-  in  the  sump,  and  concrete  placed  around  same  under 


"f?0ds,  4  C.foC.  ^  ,Wetied  Fabric 


Fig.  153.— Falsework  and  Girders,  Tank  for  American  Steel  &  Wire 
Company. 

continuous  pumping,  so  that  the  space  above  the  flange  was  kept 
dry  until  the  concrete  was  set.  Then  a  cap  was  placed  over 
the  upper  end  of  the  nipple  in  the  tank.  Thimbles  were  left 
in  the  tank  for  intake  and  discharge  pipes.  The  cost  of  the 


TANKS,  BINS,  GRAIN  ELEVATORS.  367 


Fig.  154.—-Construction  of  Intake  Tank,  LaSalle.  111. 


368  REINFORCED    CONCRETE. 

tank  was  about  $1,300.00,  or  1.6  cts.  per  gallon,  the  remarkable 
cheapness  being  due  to  the  fact  that  no  forms  were  required  for 
the  sides,  and  that  very  little  trouble  was  experienced  with 
pumping. 

Tank  for  American  Steel  &  Wire  Co.,  Cleveland,  O. — Fig. 
151  shows  a  cross-section  and  Fig.  152  the  plan  of  a  tank  built 
by  the  ^author  for  the  American  Steel  and  Wire  Company  at  the 
Emma  Furnace,  Cleveland,  Ohio.  This  tank  is  18  ft.  in  diameter 
and  24  ft.  high,  the  sides  being  3  ins.  thick,  the  bottom  4  ins", 
and  the  roof  2Vz  ins.  The  capacity  is  45,000  gallons,  and  it 
cost  $2,500.00,  which  is  5%  cts.  per  gallon.  It  was  built  in  the 
winter,  and  the  floor  of  the  tank  was  on  a  pedestal  40  ft.  above 
the  ground.  The  floor  consisted  of  girders  shown  in  Fig.  153. 
The  reinforcement  consisted  of  an  electrically  welded  fabric  of 
Ix6-in.  mesh  used  for  distributing  rods,  and  annular  rings  of 
from  %  to  */4  ins.  diameter  steel  for  carrying  rods,  which  were 
tied  to  the  fabric  every  9  ins.  by  means  of  No.  18  annealed  wire. 
In  the  roof  the  sheets  of  fabric,  62%  ins.  wide,  overlapped  one 
another  and  were  carefully  tied  down  by  means  of  No.  18  wire. 

After  the  tank  was  completed  and  filled  with  water  a  slight 
leakage  was  found  in  the  side  of  the  tank,  but  after  one  week 
had  elapsed  the  tank  was  perfectly  tight  through  silting. 

Forms  for  an  Intake  Tank. — Fig.  154  shows  how  concrete 
was  kept  moist  and  also  protected  against  freezing,  in  the  con- 
struction of  an  intake  tank,  which  was  sunk  into  a  river  bank 
near  La  Salle.  111.,  by  the  author  some  years  ago.  The  tank, 
which  consisted  of  a  reinforced  concrete  cylinder,  was  jetted 
down  as  fast  as  it  was  built,  the  concreting  being  done  at  the 
same  level  while  the  tank  was  sinking.  Fig.  155  shows  the 
manner  of  raising  the  forms. 

Battery  Vaults.— The  author  has  manufactured  a  large 
number  of  battery  vaults,  4  ft.  diameter  by  6  ft.  high,  for  block 
signal  purposes  on  railroads.  These  vaults  were  lj/2  ins.  thick 
at  bottom,  sides  and  roof,  with  a  manhole  cover  and  frame. 
The  reinforcement  consisted  of  a  wire  fabric  for  the  sides  and 
%-in.  rods  with  wire  fabric  for  the  top  and  bottom.  The  mor- 
tar consisted  of  1  Portland  cement  to  3%  coarse,  sharp  sand, 


TANKS,  BINS,  GRAIN  ELEVATORS. 


369 


Fig.   155.— Manner  of  Raising  Forms,  Intake  Tank,  LaSalle,  111. 


370  REINFORCED    CONCRETE. 

and  the  tanks  were  plastered  on  detachable  outside  molds,  and 
made  perfectly  water-tight.  Similar  tanks  are  now  manufac- 
tured by  Trusswall  Mfg.  Co.,  Kansas  City,  Mo. 

BINS  AND   GRAIN   ELEVATORS. 

The  designing  of  grain  elevators  and  storage  structures  is  a 
specialty  regarding  which  little  literature  is  at  hand,  as  it  re- 
quires a  practical  knowledge  not  generally  possessed  by  engi- 
neers. The  author  having  had  over  20  years'  experience  in  the 
'  design  and  construction  of  grain  elevators,  and  being  the  first 
designer  of  reinforced  concrete  grain  elevators  in  the  United 
States,  here  adds  some  remarks  and  suggestions  relative  to  cal- 
culations and  constructions  in  this  special  line,  based  upon  ex- 
perience of  his  own,  as  well  as  that  of  his  confreres  in  elevator 
construction,  which  has  come  under  his  observation. 

The  researches  and  writings  of  Mr.  J.  A.  Jamieson,  the  well- 
known  elevator  builder  of  Montreal,  are  particularly  valuable 
and  agree  with  the  ideas  of  the  author. 

Action  of  Grain  Flowing  From  a  Bin. — If  grain  is  allowed 
to  run  from  a  spout  to  a  floor  it  will  pile  up  until  its  slope 
reaches  a  certain  angle  called  the  angle  of  repose,  when  the 
grain  will  slide  down  the*  surface  of  the  cone.  If  a  hole  be 
cut  in  the  side  of  a  bin  the  grain  will  flow  out  until  the  open- 
ing is  blocked  up  by  the  outflowing  grain.  There  is  no  ten- 
dency for  the  grain  to  spout  up  as  in  the  case  of  fluids.  If 
grain  be  allowed  to  flow  from  an  opening  it  flows  at  a  con- 
stant rate,  which  is  independent  of  the  head  and  varies  approxi- 
mately as  the  cube  of  the  diameter  of  the  orifice.  The  law  of 
grain  pressure  has  been  studied  by  several  engineers  and  as  a 
result  has  been  fairly  well  established. 

Bridging  Action  of  Grain  in  a  Bin. — It  has  been  found 
that  in  storing  materials  in  bulk  a  certain  bridging  takes 
place  to  such  an  extent  that  at  quiescent  loads  the  lateral  pressure 
becomes  practically  constant,  and  accordingly  the  weight  of  the 
contents  of  a  bin  partly  rests  on  the  bin  walls. 

.  Table  of  Grain  Pressure. — Table  LXXIII  is  taken  from 
Mr.  J.  A.  Jamieson's  tests  on  the  Canadian  Northern  elevator  at 


TANKS,  BINS,  GRAIN  ELEVATORS. 


371 


Port  Arthur,  Ont.,  which  had  cribbed  wooden  bins  built  of  lami- 
nated planks,  2x6  ins.  to  2x10  ins.  The  lateral  and  vertical  pres- 
sures are  given  for  heights  to  65  ft.  in  a  bin  13  ft.  4  ins.  x  13 
ft.  4  ins. 

TABLE  LXXIII. — GRAIN  PRESSURE  IN  DEEP  BINS.* 


Height 
in 
Feet. 

Lateral  Pressure  in  Lbs. 

Vertical  Pressure  in  Lbs. 

Height 
in 
Feet. 

Per  sq.  in. 

Total  per  ft. 
section. 

Per  sq.  in. 

Wt.  on  bottom. 

1 

.347 

8,900 

1 

2 

67 

17,152 

2 

3 

0.22 

1,690 

95 

24,320 

3 

4 

0  43 

3,302 

1.21 

30,916 

4 

5 

0.61 

4,685 

1.45 

37,120 

5 

6 

0.80 

6,144 

1.67 

42,752 

6 

7 

0.95 

7,296 

1.87 

47,872 

7 

8 

.08 

8,294 

2.05 

52,480 

8 

9 

.19 

9,139 

2.22 

56,832 

9 

10 

.28 

"9,830 

2  37 

60,672 

10 

11 

.40 

10,752 

2  51 

64,256 

11 

12 

.50 

11,520 

2.64 

67,584 

12 

13 

1.58 

12,134 

2.76 

70,656 

13 

14 

1.66 

12,749 

2.87 

73,472 

14 

15 

1.75 

13,340 

2.97 

76,032 

15 

16 

1.81 

13,901 

3  07 

78,592 

16 

17 

1.90 

14,592 

3.17 

81,152 

17 

18 

1.97 

15,130 

3.26 

83,456 

18 

19 

2.00 

15,360 

3.34 

85,504 

19 

20 

2  05 

15,744 

3.42 

87,552 

20 

21 

2.12 

16,281 

3.50 

89,660 

21 

22 

2.18 

16,742 

3.57 

91,392 

22 

23 

2.21 

16,973 

3.63 

92,928 

23 

24 

2.30 

17,664 

3.70 

94.720 

24 

25 

2.34 

17,971 

3.76 

96,256 

25 

26 

2.37 

18,202 

3.81 

97,536 

26 

27 

2  40 

18,432 

3.85 

98,560 

27 

28 

2.41 

18,509 

3.89 

99,584 

28 

29 

2.43 

18,662 

3.93 

100  608 

29 

30 

2  45 

18,816 

3.97 

101,632 

30 

31 

2  50 

19,200 

4.02 

102,912 

31 

32 

2.51 

19,277 

4.05 

103,680 

32 

33 

2.52 

19,354 

4.0-8 

104,448 

33 

Ratio  of  Grain  to  Liquid  Pressure. — Figure  156  is  derived 
from  experiments  by  Mr.  J.  A.  Jamieson  and  closely  con- 
forming to  Janssen's  formula: 


372 


REINFORCED    CONCRETE. 


in  which 
L  =  lateral  pressure  of  grain  in  Ibs.  per  sq.  ft. 

TABLE  LXXIII,  (Continued).— GRAIN  PRESSURE  IN  DEEP  BINS. 


Height 
in 
Feet. 

Lateral  Pressure  in  Lbs. 

Vertical  Pressure  in  Lbs. 

Height 
in 
Feet. 

Per  sq.  in. 

Total  per  ft. 
section. 

Per  sq.  in. 

Wt.  on  bottom. 

34 

2.53 

19,430 

4.11 

105,216 

34 

35 

2.55 

19,584 

4.15 

106,240 

35 

36 

2.58 

19,814 

4.17 

106,752 

36 

37 

2.60 

19,968 

4.19 

107,264 

37 

38 

2.61 

20,045 

4.24 

108,544 

38 

39 

2.615 

20,083 

4.26 

109,056 

39 

40 

2.62 

20,122 

4.28 

109,568 

40 

41 

2.63 

20,198 

4.30 

110,080 

41 

42 

2.64 

20,275 

4.33 

110,848 

42 

43 

2  65 

20,352 

4   35 

111,360 

43 

44 

2.66 

20,429 

4.37 

111,872 

44 

45 

2.67 

20,506 

4.38 

112,128 

45 

46 

2.68 

20,582 

4.39 

112,384 

46 

47 

2.69 

20,659 

4.41 

112,896 

47 

48 

2.70 

20,736 

4.41 

112,896 

48 

49 

2.70 

20,736 

4.44 

113,664 

49 

50 

2.70 

20,736 

4.45 

113,920 

50 

51 

2.70 

20,736 

4.46 

114,176 

51 

52 

2.71 

20,813 

4.47 

114,432 

52 

53 

2.71 

20,813 

4.48 

114,688 

53 

54 

2.71 

20,813 

4.49 

114,944 

54 

55 

2.72 

20,890 

4.50 

115,200 

55 

56 

2.72 

20,890 

4.51 

115,456 

56 

57 

2.73 

20,966 

4.52 

115,712 

57 

58 

2.74 

21,043 

4.52 

115,712 

58 

59 

2.75 

21,120 

4.55 

116,220 

59 

60' 

2.76 

21,197 

4.55 

116,220 

60 

61 

2.77 

21,274 

4.55 

116,220 

61 

62 

2.77 

21,274 

4.55 

116,220 

62 

63 

2.77 

21,274 

4.55 

116,220 

63 

64 

2.77 

21,274 

4.55 

116,220 

64 

65 

2.77 

21,274 

4.55 

116,220 

65 

area  of  bin  in  sq.  ft. 

=  — '—; —          c,.    =  hydraulic  radius. 

circumference  of  bin 

=  the  base  of  Naperian  logarithms  =  2.718281. 


TANKS,  BINS,  GRAIN  ELEVATORS.  373 


.50 


,30 


4 
I 

JO 


£>       34       5,6        7       d       ?      JO 
Valves  0f  % 

Fig.  156.— Graphic  Diagram  of  Wheat  Pressure  in  Bins. 
//'  =  coefficient  of  friction  of  grain  on  cement  =  0.41667. 
The  values  of  K  are  shown  for  different  values  of 


374  REINFORCED    CONCRETE. 

h_ 
b 

which  is  the  ratio  of  the  depth  of  grain  to  the  side  of  a  square 
bin,  or  least  side  of  a  rectangular  bin. 

The  following  notation  is  used  in  constructing  the  diagram: 
Angle  of  repose  =  28°. 
Coefficient  of  friction  =  0.41667. 
Lateral  pressure  —  0.6  vertical  pressure. 
h  =  height  or  depth  of  grain. 
b  =  least  side  of  bin. 

K==  ratio  of  actual  grain  pressure  to  liquid  pressure. 
w  =  weight  of  wheat  =  50  Ibs.  per  cu.  ft. 
Side  pressure  per  sq.  it.==Kwh. 
Bottom  pressure  at  any  depth  =  1.667  Kwh. 

Maximum  bottom  pressure  occurs  when  £-  =  3.5. 

Maximum  bottom  pressure  per  sq.  ft.  =  wb. 

Example. — Let  it  be  required  to  find  the  vertical  and  hori- 
zontal pressures  at  the  bottom  of  a  bin  10  ft.  square  and  40  ft. 
deep. 

h 

r  =  4 

From  the  curve, 
K  =  .149. 

Side  pressure  =Kwh  =  .U9  X  50  X  40  •=  298  Ibs.  per  sq.  ft. 
Bottom  pressure  =  1.667  Kwh==4Q7  Ibs.  per  sq.  ft. 
Vertical  load  carried  by  side  walls  =  200,000  —  (497  X100)  = 
150,300  Ibs. 

Vertical  Pressure. — The  vertical  pressure  in  a  deep  grain 
tin  is  calculated  as  follows:  The  grain  supported  by  the  side 
walls  is  equal  to  the  lateral  pressure  multiplied  by  the  coeffi- 
cient of  friction  of  the  grain  on  the  bin  wall.  The  grain  car- 
ried on  the  bottom  of  the  bin  is  equal  to  the  total  weight  of 
grain,  minus  the  weight  carried  by  the  side  walls.  The  bot- 
tom pressure  is  not  uniformly  distributed,  but  is  a  minimum  at 


TANKS,  BINS,  GRAIN  ELEVATORS. 


375 


the  side  walls  and  a  maximum  at  the  center.  The  grain  mass 
producing  bottom  pressure  may  be  represented  by  a  portion 
of  an  ellipsoid  of  revolution  with  the  major  axis  of  the  el- 
lipse vertical. 

Ratio  Between  Lateral  and  Vertical  Pressure. — The  value 
of  the  ratio  between  lateral  and  vertical  pressure  in  a  bin, 

• 

is  not  a  constant  for  grain  in  a  bin  at  different  depths,  being 
greater  for  small  than  for  large  depths  of  grain  and  varying 
with  different  bins  and  different  grains.  Average  values  of  k 
for  wheat  and  rye  are  given  in  Table  LXXIV. 


TABLE  LXXIV. — VALUES  OP  fe=— IN  DIFFERENT  BINS. 

V 


Bins. 

L 

k=— 
V 

Wheat. 

Rye. 

Cribbed  bin 

0.4    to  0.5 
0.4    to  0.5 
0.34  to  0.46 
0.3 
0.3    to  0.35 

0.23  to  0.32 
0.3    to  0.34 
0.3    to  0.45 
0.23  to  0.28 
0.3 

Ringed  cribbed  b 
Small  plank  bin 

Large  plank  bin  . 

Reinforced  concr 

etc  bin    .... 

The  Coefficient  of  Friction. — The  coefficient  of  friction  of 
grain  on  concrete  is  0.4  to  0.425,  according  to  roughness  of  the 
concrete. 

The  coefficient  of  friction  of  wheat  on  wheat  is  0.532,  or 
tan  28°.  Table  LXXV,  coefficients  of  friction  for  various  ma- 
terials, is  compiled  by  Mr.  Wilfred  Airy  as  a  result  of  his  ex- 
periments, printed  in  the  proceedings  of  Inst.  of  Civ.  Eng.,  Vol. 
CXXXI,  1897. 


376  REINFORCED    CONCRETE. 

TABLE  LXXV. — COEFFICIENTS  OF  FRICTION  OF  VARIOUS  MATERIALS. 


Weight 
loose. 

Coefficient  of  Friction. 

Grain 
on 
grain. 

Grain  on 
rough 
wood. 

Grain  on 
smooth 
wood. 

Grain 
on 
iron. 

Grain 
on 
cement. 

Wheat  

49 

,466 

.412 

.361 

.414 

.444 

Barley  

39 

.507 

.424 

.325. 

.376 

.452 

Oats   ...    . 

28 

.532 

.450 

.369 

.412 

.466 

Corn  .  .  . 

44 

.521 

.344 

.308 

.374 

.423 

Beans.  

46 

.616 

.435 

.322 

.366 

.442 

Peas   ..... 

56 

.472 

.287 

.268 

.263 

.296 

Tares  

49 

.554 

.424 

.359 

.364 

.394 

Flaxseed  

41 

.456 

.407 

.308 

.339 

.414 

rr 


Mr/) 


j 


Pressure  of  Coal  in  Bins. — Tables 
LXXVI  and  LXXVII,  giving  the  pres- 
sure of  coal  in  bins,  are  taken  from  the 
paper   by   Mr.    R.    W.   Dull,   printed   in 
Enginering   News,   July  21,    1904.     See 
Fig.  157.     In  the  formulas, 
0  =  angle  of  repose 
0'=  angle    of    friction   between    ma- 
terial  and   bin  wall 
—  angle  between  direction  of  thrust 

and  normal  to  bin  wall 
P  =  total  thrust  against  bin  wall  per 

ft. 

N ^=  horizontal  component  of  P 
8'— angle  of  slope  of  surface  of  material. 
For  both  the  tables, 

Col.  1  gives  normal  component  of  total  pressure  on  vertical 
side,  when  surface  is  level. 


Fig.  157. 


cos 


2  wh* 


where 


sin  (0  4-  0 ')    sin 
cos  0 


..:'(70) 


TAXKS.  BINS,  GRAIN  ELEVATORS. 


377 


TABLE  LXXVI. — TOTAL  PRESSURE  AT  DEPTH  h  FOR  BITUMINOUS  COAL. 

Wt.  per  c,u.  ft.  =  50  Ibs.    •  Angle  of  repose  =  0  =  35°. 

Pressures  for  a  section  of  material  1  ft.  wide. 


1 

2 

3 

4 

5 

6 

Depth 
in 
feet. 

rr 
*  i 

A 

h 

rf 
* 

$f 

h    , 

n\ 
?P 

A 

dr 

1± 

IT 

£ 

ur 

tT 

& 

i      1 

8 

fe 

* 

0'=18° 

£'=0 

5  —  0 

3=0 

8=  0 

3=0 

1 

5.83 

6.75 

16.75 

20.5 

4.27 

5.13 

2 

23.32 

27.00 

67.00 

82.0 

17.1 

20.5 

3 

52.47 

60.75 

150.75 

184.5 

38.4 

46.2 

4 

93.4 

108.00 

268.00 

328 

68.3 

82.0 

5 

145.7 

168.75 

418.75 

513 

107 

128.0 

6 

209.4 

243 

603 

738 

156 

184.5 

7 

286 

333 

821 

1,005 

209 

257 

8 

373 

432 

1,072 

1,312 

273 

328 

9 

472 

547 

1,357 

1,661 

346 

415 

10 

583 

675 

1.675 

2,050 

427 

513 

11 

705 

817. 

2,027 

2,481 

516 

615 

12 

840 

972 

2,412 

2,952 

615 

738 

13 

985 

1,141 

2,831 

3,465 

722 

866 

14 

1,143 

1,323 

3,283 

4,018 

838 

1,005 

15 

1,312 

1,519 

3,769 

4,613 

960 

1,152 

16 

1,492 

1,728 

4,288 

5,248 

1,093 

1,311 

17 

1,685 

1,951 

4,841 

5,945 

1,232 

1,480 

18 

1,889 

2,187 

5,427 

6,642 

1,382 

1,660 

19 

2,105 

2,437 

6,047 

7,400 

1,541 

1,852 

20 

2,332 

2,700 

6,700 

8,200 

1,708 

2,052 

21 

2,571 

2,977 

7,387 

9,041 

1,883 

2,262 

22 

2,821 

3,267 

8,102 

9,922 

2,065 

2,483 

23 

3,084 

3,571 

8,861 

10,845 

2,259 

2,560 

24 

3,358 

3,888 

9,648 

11,808 

2,460 

2,810 

25 

3,644 

4,219 

10,469 

12,813 

2,669 

3,206 

26 

3,941 

4,563 

11.323 

13,858 

2,887 

3,468 

27 

4,250 

4,923            12.211 

14,945 

3,113 

3,740 

28 

4,570 

5,292 

13,142 

16,072 

3,348 

4,022 

29 

4,903 

5,677 

14,087 

17,241 

3,591 

4.314 

30 

5.247 

6,075 

15.075 

18.450 

3.843              4,617 

378 


REINFORCED    CONCRETE. 


TABLE  LXXVII. — TOTAL  PRESSURE  AT  DEPTH  h  FOR  ANTHRACITE  COAL. 

Wt.  per  cu.  ft.  =  52  Ibs.     Angle  of  repose =  0  =  27°. 

Pressures  for  a  section  of  material  1  ft.  wide. 


1 

2 

3 

4 

5 

6 

Depth 

" 

r" 

A 

in 
feet. 

rr 

1 

T  ^ 

l^\ 

ih 

i.e- 

h  ^ 

i 

rt 

LL 

B' 

1  1  . 

4- 

h 

#'-«• 

0'=0 

•-* 

3=  0 

5=  0 

5=0 

1 

8.39 

9.75 

20.05 

23.17 

6.38 

2 

33.5 

39.0 

82.0 

93.3 

25.5 

3 

75.5 

87  0 

184.5 

208.6 

57  5 

4 

134  2 

156 

328 

371 

102.0 

5 

210 

244 

513 

579 

159.5 

6 

302 

351 

738 

834 

230 

7 

411 

478 

1,005 

1,135 

313 



8 

536 

624 

1,312 

1,482 

402 

9 

680 

790 

1,661 

1,876 

517 

10 

839 

975 

2,050 

2,317 

638 

11 

1,014 

1,180 

2,481 

2,802 

773 

925 

12 

1,209 

1,405 

2,952 

3,340 

920 

1,100 

13 

1,418 

1,648 

3,465 

3,918 

1,080 

1,290 

14 

1,643 

1,910 

4,018 

4,540 

1,250 

1,497 

15 

1,887 

2,193 

4,613 

5,220 

1,436 

1,720 

16 

2,145 

2,500 

5,248 

5,930 

1,636 

1,953 

17 

2,421 

2,808 

5,945 

6,696 

1,845 

2,207 

18 

2,718 

3,160 

6,642 

7,507 

2,064 

2,471 

19 

3,030 

3,521 

7,400 

8,363 

2,310 

2,758 

20 

3,350 

3,902 

8,200 

9,268 

2,554 

3,053 

21 

3,700 

4,303 

9,041 

10,218 

2,820 

3,372 

22 

4,061 

4,718 

9,922 

11,214 

3,086 

3,701 

23 

4,438 

5,156 

10,845 

12,257 

3,372 

4,040 

24 

2,833 

5,611 

11,808 

10,346 

3,680 

4,398 

25 

5,244 

6,097 

12,813 

14,481 

3,985 

4,770 

26 

5,672 

6,600 

13,858 

15,663 

4,521 

5,160 

27 

6,116 

7,112 

14,945 

16,891 

4,650 

5,560 

28 

6,578 

7,638 

16,072 

18,165 

5,000 

5,979 

29 

7,056 

8,202 

17,241 

19,486 

5,370 

6,421 

30 

7,551 

8,775 

18,450 

20,853 

5,742 

6,880 

TANKS,  BINS,  GRAIN  ELEVATORS.  379 

Col.  2  gives  pressure  against  vertical  plane  AB  when  friction 
is  not  considered,  i.  e.,  is  taken  as  —O. 

wh*  f  (f>\ 

N  =  ~2~  tan2  (^45  —  -y  j  ............  (71) 

Col.  3  gives  normal  component  of  total  pressure  on  vertical 
side  when  surface  is  surcharged  to  the  angle  of  repose,  and  the 
bin  is  unlimited  in  horizontal  extent. 


N  =  cos2  </>  ~2~  ................  (72) 

Col.  4  gives  the  same  as  Col.  3,  except  that  angle  of  friction 
is  neglected. 

wh* 
N  =  cos  0  ~2~  ...............  (73) 

Col.  5  gives  normal  component  of  total  pressure  on  vertical 
side  when  material  slopes  downward  along  angle  of  repose. 


/cos  (J>\*wh-  sin(0  +0')  sin  (0  +  5) 

-\-^T)    T   where  »->|-      cos  »'  cos   »         - 

Col.  6  gives  same  as  Col.  5,  except  that  friction  is  neglected. 


cos    (t>\zwh*  sin  </)  sin  (0  +  5  ) 

-       -  .....  (75) 


Weight,  Angle  of  Repose  and  Angle  of  Friction  of  Va- 
rious Materials.  —  Table  LXXVIII  gives  the  weight  and 
angle  of  repose  of  coal,  coke,  ashes  and  ore  as  compiled  from 
various  authorities,  and  Table  LXXIX,  gives  the  angle  of  fric- 
tion of  coal,  ashes,  coke  and  sand  on  bin  walls. 

Capacity  of  Bins.—  Tables  LXXII,  page  359,  gives  the  ca- 
pacity of  tanks  in  gallons.  These  values  may  be  changed  to 
bushels  by  multiplying  the  number  of  cubic  feet  by  0.8,  the  result 
being  the  capacity  in  bushels. 


380 


REINFORCED    CONCRETE. 


TABLE  LXXVIII. — WEIGHT  AND  ANGLE  OF  REPOSE  OF  COAL,  COKE, 
ASHES  AND  ORE. 


Material. 

Wt.  in  Ibs. 
per  cu.  ft. 

Angle  of 
reoose  in 
degrees. 

Authority. 

Bituminous  coal  
Anthracite  coal 

50 
47 
47  to  56 
52 

35 
35 

"27"  ' 

Link  Belt  Machinery  Co. 
Link  Belt  Engineering  Co. 
Cambria  Steel  Co. 
Link  Belt  Machinery  Co. 

'    fine...    . 

52.1 

'  52  to  56'  ' 

27 
27 

Link  Belt  Engineering  Co. 
K.  A.  Muellenhoff. 
Cambria  Steel  Co. 

Slaked  coal  

53 

45 
37.5 

Wellman-Seaver-Morgan  Co. 
Gilbert  &  Barth. 

Coke              

23  to  32 

Cambria  Steel  Co 

Ashes  

40 

40 

Link  Belt  Machinery  Co, 

Ashes  soft  coal  

40  to  45 

Cambria  Steel  Co 

35 

Wellman-Seaver  -Morgan  Co 

TABLE  LXXIX. — ANGLE  OF  FRICTION  OF  MATERIALS  ON  BIN  WALLS. 


Material. 

Steel  plate. 
0  '  in  degrees. 

Wood  cribbed 
0  '  in  degrees. 

Concrete. 
0  '  in  degrees. 

Bituminous  Coal  
Anthracite  Coal 

18 
16 

35 
25 

35 
27 

Ashes  

31 

40 

40 

Coke            .    . 

25 

40 

40 

Sand  

18 

30 

30 

Conclusions. — The  following  interesting  conclusions  are 
drawn  by  Professor  Ketchum  from  experiments  on  grain  press- 
ure made  by  Messrs.  Jamieson,  Airy,  Prante,  Pleissner,  Lufft, 
Bovey,  Janssen  and  others: 

(1)  The  pressure  of  grain  on  bin  walls  and  bottom  follows 
a  law  which  for  convenience  will  be  called  the  law  of  semi-fluids, 
and  which  is  entirely  different  from  the  law  of  the  pressure  of 
fluids. 

(2)  The  lateral  pressure  of  grain  on  bin  walls  is  less  than 
the  vertical  pressure  (0.3  to  0.6  of  the  vertical  pressure,  depend- 
ing on  the  grain,   etc.),   and   increases  very  little  after  a  depth 
of  2%  to  3  times  the  width  or  diameter  of  the  bin  is  reached. 

(3)  The  ratio  of  lateral  to  vertical  pressure,  k,  is  not  a  con- 
stant, but  varies  with  different  grains  and  bins.      Its  value  can 
be  determined  only  by  experiment. 


TANKS,  BINS,  GRAIN  ELEVATORS.  381 

(4)  The  pressure  of     moving  grain  is  very  slightly  greater 
than    the    pressure    of   grain    at    rest    (maximum    variation    for 
ordinary  conditions  being  probably  10%. 

(5)  Discharge   gates  in  bins   should  be  located  at  or  near 
the  center  of  the  bin. 

(6)  If  the  discharge  gates  are  located  in  the  sides  of  the 
bins,    the    lateral    pressure    due    to    moving    grain    is    decreased 
near  the  discharge  gate  and  is  materially  increased  on  the  side 
opposite  the  gate.     For  common  conditions  this  increased  pres- 
sure may  be  2  to  4  times  the  lateral  pressure  of  grain  at  rest. 

(7)  Tie  rods  decrease  the  flow,  but  do  not  materially  affect 
the  pressure. 

(8)  The  maximum  lateral  pressures  occur  immediately  after 
filling,   and  are  slightly  greater  in  a  bin  filled  rapidly  than  in 
a  bin  filled  slowly.      Maximum  lateral  pressures  occur  in  deep 
bins  during  filling. 

(9)  The  calculated  pressures  by  either  Janssen's  or  Airy's 
formulas  agree  very  closely  with  actual  pressures. 

(10)  The  unit  pressures  determined  on  small  surfaces  agree 
very  closely  with  unit  pressures  on  large  surfaces. 

(11)  Grain  bins  designed  by  the  fluid  theory  are  in  many 
cases  unsafe,  as  no  provision  is  made  for  the  side  walls  to  carry 
the  weight  of  the  grain  and  the  walls  are  crippled. 

(12)  Calculation  of  the  strength  of  wooden  bins  that  have 
been  in  successful  operation  shows  that  the  fluid  theory  is  un- 
tenable, while  steel  bins  designed  according  to  the  fluid  theory 
have  failed  by  crippling  the  side  plates. . 

Classification  of  Grain  Elevators. — Grain  elevators  are  di- 
vided into  several  classes.  There  are  terminal  elevators,  trans 
fer  and  cleaning  elevators,  storage  houses,  and  station  eleva- 
tors. They  are  also  divided  into  working  houses  and  storage 
houses.  The  station  elevators  generally  run  from  5,000  to 
100,000  bushels'  capacity,  and  are  combined  working  and  storage 
houses.  The  working  house  contains  all  the  elevating,  weigh- 
ing, cleaning,  and  shipping  machinery.  The  storage  elevator 
generally  only  contains  receiving  and  shipping  machinery,  con- 


382  REINFORCED    CONCRETE. 

sisting  of  belt  conveyors.  From  the  station  elevators  in  the 
country,  the  grain  is  shipped  by  rait  either  directly  to  terminal 
elevators  for  export  or  to  transfer  and  cleaning  houses  to  be 
mixed,  graded,  cleaned,  and  transferred  to  other  railroads.  A 
transfer  and  cleaning  elevator  is  generally  termed  a  three-car 
house,  four-car  house,  or  a  six-car  house,  according  to  the 
number  of  grain  cars  that  can  be  unloaded  simultaneously. 
The  storage  capacity  of  these  houses  is  generally  very  limited, 
running  from  75,000  to  250,000  bushels;  The  terminal  elevator 
consists  either  of  a  combined  storage  or  working  house  in  one 
structure  or  a  storage  house  and  a  working  house  for  the  re- 
ceipt and  discharge  of  grain.  The  capacity  of  a  terminal  eleva- 
tor generally  runs  from  300,000  to  3,000,000  bushels  or  more. 

Comparative  Cost  of  Timber  and  Reinforced  Concrete 
Elevators. — For  many  years  wooden  cribbing  was  used  in 
square  bins  for  the  storage  of  grain  and  owing  to  their  inflam- 
mable nature,  a  heavy  insurance  charge  was  necessary.  While 
such  storage  elevators  could  be  built  from  8  to  15  cts.  per 
bushel  capacity  in  inverse  proportion  to  the  size,  the  charges 
for  insurance  and  deterioration  were  quite  heavy.  Reinforced 
concrete  storage  houses  which  cost  from  14  to  20  cts.  per 
bushel  capacity  for  large  sizes  and  also  in  inverse  proportion 
to  their  capacity  need  not  carry  any  charges  for  insurance  of 
the  structure  nor  for  deterioration,  and  have  now  become  a  fa- 
vorite mode  of  construction.  Working  houses  which  cost  from 
20  to  30  cts.  per  bushel  in  wood  cost  practically  twice  as  much  in 
concrete.  This  is  due  to  the  fact  that  for  storage  houses  cir- 
cular bins  can  be  used,  which  is  by  far  the  most  economical 
shape  for  the  storage  of  materials,  while  for  work  houses  square 
bins  are  more  practical,  but  of  considerably  higher  expense. 

Cement  Storage  Tanks,  Illinois  Steel  Co.,  South  Chicago, 
111. — The  author  has  invented  and  patented  a  fire-proof 
"cluster-tank  construction,"  the  first  application  of  which  was 
made  in  the  construction  of  cement  storage  tanks  for  the  Illi- 
nois Steel  Co.  at  South  Chicago,  111.,  in  1901.  Fig.  158  shows 
sectional  views,  Fig.  159  the  plan,  and  Fig.  160  details  of  the 
construction.  The  tanks  are  25  ft.  in  diameter,  29  ft.  center  to 


TANKS,  BINS,  GRAIN  ELEVATORS. 

V- 


383 


Vertical 


Section. 


Fig.    158.— Section   of   Cement   Storage   Bins,    Illinois    Steel   Co., 
Chicago. 


384 


REINFORCED    CONCRETE. 


^"-  —  -Sec1-ional  Plan.' — •"' 

Fig.  159.— Plan  of  Cement  Storage  Bins,  Illinois  Steel  Co.,  Chicago, 


TANKS,  BINS,  GRAIN  ELEVATORS. 


385 


center,  inclosing  a  center  tank,  which  makes  the  cluster  con- 
struction of  five  tanks,  the  space  between  each  pair  of  adjacent 
walls  being  closed  by  a  cylindrical  shaft  30  ins.  in  diameter,  the 
entire  structure  being  monolithic.  The  foundation  is  on  made 
ground  and  consists  of  a  mat  66  ft.  square,  3  ft.  thick  and  re- 
inforced by  a  netting  of  %-in.  steel  rods  of  9-in.  mesh  tied  to- 
gether at  their  intersections  by  No.  18  wire.  Upon  this  con- 


"w 


Detail    of    Piers. 


Detail    of     Central    Tar*     Bottom. 


Fig.  160. — Details  of  Cement  Storage  Bins,  Illinois  Steel  Co., 
Chicago. 

crete  bed  is  a  series  of  piers  12  ft.  6  ins.  high  and  1  ft.  10  ins. 
thick.  Those  near  the  outer  circumference  of  the  tanks  are  3 
ft.  5  ins.  long,  but  those  supporting  the  corners  of  the  tanks 
are  7  ft.  10  ins.  long.  The  smaller  piers  have  4  steel  rails,  the 
larger  6  or  8  rails,  embedded  in  the  concrete.  The  rails  are 
connected  by  splicing  bars  riveted  to  them,  and  rest  on  1%-in. 
steel  plates  embedded  in  the  concrete  floor  about  15  ins.  below 
the  surface.  The  piers  are  capped  with  similar  plates  and  sup- 


386  REINFORCED    CONCRETE. 

port  concrete  steel  girders  15  ins.  deep  and  4  ft.  wide  with 
vertical  openings  at  intervals  for  the  discharge  pipes.  Through 
each  girder  run  four  horizontal  lines  of  steel  rods  near  the 
top,  and  four  other  lines  bent  to  form  truss  rods  with  sheets  of 
wire  netting  on  each  side  of  each  pair  of  rods.  The  cylindrical 
tanks  53  ft.  6  ins.  high  rest  upon  this  system  of  girders,  the  base 
being  13  ft.  9  ins.  above  the  level  of  the  concrete  floor.  The 
walls  are  7  ins.  thick  in  the  lower  part  and  5  ins.  in  the  upper 
part  The  reinforcement  consists  of  a  continuous  sheet  of  net- 
ting of  No.  9  Clinton  wire  cloth  Ix4-in.  mesh.  Around  this 
alternately  inside  and  outside  are  horizontal  rings  of  rods  4  ins. 
apart  tied  to  the  netting  by  wire.  These  rods  vary  in  diameter 
from  1  in.  near  the  base  to  %  in.  near  the  top,  which  is  finished 
with  a  ring  formed  by  a  5-in.  Z  bar  supporting  the  conical  roof. 
The  latter  is  2  ins.  thick  with  a  manhole  at  the  edge,  and  an 
opening  at  the  apex  for  the  spout.  In  place  of  hoppering  the 
bin  bottoms  in  an  inverted  cone  as  usual,  these  hoppers  were 
reversed,  the  apex  pointing  upwards  so  as  to  prevent  any 
trouble  in  the  discharge  of  the  cement  by  bridging.  The  dis- 
charge openings  around  the  circumference  are  15x48  ins.  and 
each  serves  a  sacking  spout.  The  conical  bottom  is  4  ins.  thick, 
reinforced  with  rods  and  netting.  The  foundation  concrete  and 
also  the  pier  concrete  consist  of  1  part  Portland  cement,  3  parts 
coarse  sand,  and  4  parts  of  crushed  limestone.  The  tanks  proper 
are  built  of  mortar  of  1  part  Portland  cement  and  3^4  parts 
sand,  mixed,  weighed  and  lightly  rammed  in  wooden  forms. 
The  concrete  was  poured  in  and  tamped  inside  of  the  forms, 
which  were  raised  in  45°  sections  28  ins.  high,  every  24  hours. 
Work  was  carried  on  day  and  night  until  finished.  The  elevator 
shaft  is  built  of  steel  frame  covered  with  Monier  siding  plates, 
2x5  ft.  by  %  in.  thick,  made  of  cement  mortar  and  wire  netting 
similarly  as  for  roofs. 

Canadian  Pacific  Grain  Elevator,  Port  Arthur,  Ont. — Fig. 
161  shows  a  plan  of  the  Canadian  Pacific  grain  elevator  at  Port 
Arthur,  Ont,  built  by  Barnett  &  Record  Co.  in  1904  on  the  clus- 
ter tank  principle.  There  are  nine  cylindrical  tanks  so  as  to  in- 
close four  intermediate  spaces,  the  entire  construction  being 


TANKS,  BINS,  GRAIN  ELEVATORS. 


387 


monolithic.  The  circular  bins  are  30  ft.  in  diameter  and  90  ft. 
high,  and  as  no  necessity  existed  for  making  the  intermediate 
spaces  larger,  the  tanks  were  placed  close  together  and  the 
strength  of  the  tank  connections  was  further  increased  by  plac- 
ing brace  rods  in  the  intermediate  bins.  The  walls  are  9  ins. 


•ffam.  Vertical  Rods 


H*t,  Z'Mcsh. 


Fig.    161.— Plan   of   Canadian   Pacific   Grain   Elevator,    Port   Arthur, 

Ontario. 

thick  on  foundations  24  ins.  thick  carried  down  to  footings 
resting  on  hard  pan.  The  conical  tank  bottoms  are  seated  on 
rammed  sand  fill.  Under  the  center  of  each  row  of  bins  there 
is  a  concrete  lined  conveyor  tunnel  7  ft.  wide,  7  ft.  high  and 
about  86  ft.  long.  The  concrete  used  was  1  part  Portland  cem- 


388 


REINFORCED    CONCRETE. 


ent,  3  parts  sand,  and  5  parts  Lake  Superior  gravel.  The  hori- 
zontal reinforcement  consists  of  hooping  bars  spaced  12  ins. 
apart  vertically,  the  size  of  the  bars  decreasing  from  the  bottom 
upwards.  The  bars  are  in  pairs,  one  near  each  surface  of  the 
shell.  For  the  first  15  ft.  above  the  base  their  cross-section  is  I 
sq.  in.,  for  the  next  35  ft.  it  is  .88  sq.  in.,  for  the  next  20  ft.  .75 

.........  7&,..._.  - 


Sectional   Plan  of  Forms. 

rrm 


Fig.  162.— Forms  for  Bin  Construction,  Grain  Elevator,  Port  Arthur, 

Ontario. 

sq.  in.,  and  above  that  a  cross-section  of  %  sq.  in.  Besides  the 
horizontal  bars  there  are  in  each  bin  27  vertical  bars,  spaced 
equally  distant  apart.  Where  adjacent  tanks  touch  and  have  the 
walls  thickened  accordingly,  the  two  hoops  are  clamped  to- 
gether by  2  straps  \\  x  ^  ins.  every  foot  in  height,  whose 
ends  hook  over  the  two  hoops.  There  is  also  in  this  thickened 
portion  a  horizontal  sheet  of  wire  netting  at  every  foot  in 
height.  The  concrete  walls  of  the  bins  were  made  in  cylindrical 
forms,  4  ft.  high,  as  shown  in  Fig.  162.  The  curved  surfaces  of 
the  forms  were  made  of  2-in.  vertical  planks  spiked  to  the  in- 
side and  outside  circular  chords,  which  latter  were  made  like 
arch  centers  with  four  thicknesses  of  2x8-in.  scarfed  planks 


TANKS,  BINS,  GRAIN  ELEVATORS.  389 

bolted  together  to  break  joints  and  to  make  complete  circles 
inside  the  tanks  and  circular  segments  on  outside  of  tanks.  The 
molds  were  faced  on  the  inside  with  No.  28  galvanized  steel, 
and  were  maintained  in  concentric  positions  with  a  fixed  distance 
between  them  by  means  of  8  U-shaped  steel  yokes  in  radial 
planes,  as  plainly  shown  in  the  illustration.  The  lower  ends  of 
the  vertical  yoke  posts  were  seated  on  jack-screws  and  were 
supported  on  false  work  built  up  inside  the  tanks,  as  the  walls 
progressed. 

The  Heidenreich  Concrete  Elevator,  as  here  described, 
which  was  patented  in  the  United  States  in  1901,  is  now 
replacing  nearly  all  the  large  wooden  elevators  in  the  coun- 
try— and  hundreds  have  been  built  during  the  past  decade, 
both  here  and  in  Canada — of  capacities  from  50,000  bushels 
to  4,000,000  bushels  each.  The  saving  in  insurance,  main- 
tenance and  deterioration  from  any  cause  more  than  makes 
up  for  the  difference  in  cost,  more  particularly  as  timber  prices 
are  steadily  rising. 


CHAPTER  VII. 

CHIMNEYS,  MISCELLANEOUS  DATA,  COST  KEEPING, 

ESTIMATING,  SPECIFICATIONS,  ETC. 

CHIMNEYS. 

Calculation.  —  Chimneys  are  designed  to  withstand  the 
stresses  from  their  own  weight  and  in  addition  a  wind  pressure 
generally  taken  at  50  Ibs.  per  sq.  ft.,  and  for  circular  chimneys 
this  pressure  is  applied  to  one-half  the  projected  area. 

In  Germany  and  Austria  two-thirds  the  projected  area  is 
figured,  but  only  a  wind  pressure  of  35  Ibs.  per  square  foot.  In 
cjiimneys  with  an  inner  and  an  outer  shell  only  the  outer  shell 
is  taken  into  consideration.  The  foundation  is  usually  so  ar- 
ranged that  the  dead  load  of  the  chimney  does  not  exceed  1  ton 
per  sq.  ft.  on  the  soil  and  the  combined  wind  and  dead  load 
does  not  exceed  2  tons  per  sq.  ft. 

In  calculating  the  dimensions  of  the  shell,  the  weight  is  first 
taken  into  consideration  and  the  load  divided  on  the  concrete 
and  the  steel,  in  proportion  to  the  ratio  of  the  two  moduli  of 
elasticity. 

The  wind  pressure  will  act  at  one-half  the  height  and  will 
produce  a  moment  M  about  the  center  of  the  horizontal  sec- 
tion to  be  examined.  The  pressure  in  the  extreme  fiber  C  in 
the  concrete  will  be  expressed  by  the  equation 


where  D  =  external  diameter  of  the  chimney 

7C  =  moment  of  inertia  of  the  concrete  section 
I8  =  moment  of  inertia  of  the  reinforcement 
EB 


390 


CHIMNEYS  AND  MISCELLANEOUS  DATA.        391 


be 


The  stresses  in  the  reinforcement  due  to  wind  pressure  will 


/.=   9 


nMd* 


(77) 


Where  ds  is  the  diameter  of  circle  in  which  the  steel  reinforce- 
ment is  located. 

This  calculation  may  also  be  used  for  tanks  or  towers  to  take 
care  of  wind  pressure. 

The  Core  Theory.— As  some  engineers  introduce  the  core 
theory  in  chimney  calculations,  we  will  briefly  refer  to  this  fea- 
ture. 

The  core  of  a  cross  section  is  the 
area  inside  of  which  a  force  must  be 
applied  when  the  entire  cross  section  is 
to  have  stresses  of  the  same  sign  (  + 
or  — ).  If  the  force  is  applied  outside 
the  core,  the  cross  section  will  have 
both  tension  and  compression. 
--<^^-|-  If  the  force  is  applied  in  the  circum- 

1$ U— •  J  ference  of  the  core,  the  stresses  will  go 

* <£> •--*•          as  far  as  to  zero,  but  all  will  haye  the 

same  sign. 

Hence  the   core   circumference   really 
represents    the   line   in    which    all    zero 
points  are  located. 

The  core  radius  r  is  the  section  modulus  W  divided  by  the 
area  F  (See  Fig.  163). 


Fig.  163.—  Cross- 
Section  Showing 
Neutral  Core  in 
Chimney. 


Now 

and 

hence 


w 


£)'] 


for  a  homogeneous  section. 

It  is  not  within  the  province  of  this  book  to  enter  into  the 
more  intricate  methods  of  calculations,  such  as  described  by  Dr. 
R.  Salinger  in  Beton  u.  Eisen,  1905,  pages  253  and  273,  as  the 


392  -REINFORCED    CONCRETE. 

method  herein  given  is  safe  enough  both  for  original  calcula- 
tions and  review. 

Wind  Pressure  and  Velocity. — From  experiments  made  by 
Prof.  C.  F.  Marvin  of  U.  S.  Weather  Bureau  (see  Anemometry, 
Circular  D,  second  edition,  1900)  it  is  found  that  wind  pres- 
sures are  not  so  great  as  generally  computed  and  are  quite  ac- 
curately given  by  the  following  equation : 

P  =  0.004  ^  (SF2) ."'..,' (79) 

Where  P  =  pressure  in  pounds. 

S  =  surface  in  sq.  ft. 

V  ==  corrected  velocity  of  wind  in  miles  per  hour. 

B  =  height  of  barometer  in  inches. 

For  stations  near  the  sea  level,  where  the  barometric  pres- 

r> 

sure  does  not  vary  much  from  30  ins.,  the  ratio  -^.  need  not 

be  considered.  The  relation  between  the  wind  velocity  V  in 
miles  per  hour  and  the  linear  velocity  v  of  the  cup  centers  of  an 
anemometer,  also  in  miles  per  hour,  can  be  expressed  by  the 
following  equation : 

Log  V  —  0.509  +.0,9012  log  v (80) 

and  Table  LXXX  gives  true  velocities  as  compared  with  indi- 
cated velocities,  and  corresponding  wind  pressures. 

Approximate  Mfithod  of  Calculation. — A  simple  and  safe 
approximate  method  for  calculating  chimneys  is  given  in  Beton 
und  Eisen,  1905.  Heft  X,  and  is  as  follows : 

F  =  the  cross  section  of  the  outer  shell  in  sq.  ins. 

r  —  the  mean  radius  of  cross  section  in  ft. 

As  —  cross  section  of  vertical  bars  in  sq.  ins. 
_  100Q^8 

R  =  the  lever  arm  from  the  center  of  the  chimney  to  the 
resultant  of  the  weight  in  tons  of  the  chimney  Q  and  the  wind 
pressure  W. 


CHIMNEYS  AND  MISCELLANEOUS  DATA.         393 

TABLE  LXXX. — WIND  VELOCITIES  AND  PRESSURES  AS  INDICATED  BY 

ROBINSON'S  ANEMOMETER. 

(Corrected  to  true  velocities.) 


Indi- 
cated 
veloc- 
ity. 

True  Velocity. 

+  0 

+  1 

+  2   . 

+  3 

+  4 

+  5 

+  6 

+  7 

+  8 

+  9 

0 

10 
20 
30 
40 
50 
60 
70 
80 
90 

'  'g'.e' 

17.8 
25.7 
33.3 
40.8 
48.0 
55.2 
62.2 
69.2 

5. 

13.8 
21.8 
29.6 
37.1 
44.4 
51.6 
58.7 
65.7 

6. 
14.6 
22.6 
30.3 
37.8 
45.1 
52.3 
59.4 
66.4 

6.9 
15.4 
23.4 
31.1 
38.5 
45.9 
53.0 
60.1 
67.1 

7.8 
16.2 
24.2 
31.8 
39.3 
46.6 
53.8 
60.8 
67.8 

8.7 
17.0 
24.9 
32.6 
40. 
47.3~ 
54.5 
61.5 
68.5 

10.4 

18.6 
26.5 
34.1 
41.5 
48.7 
55.9 
62.9 

11.3 

19.4 
27.3 
34.8 
42.2 
49.4 
56.6 
63.6 

12.1 
20.2 
28.0 
35.6 
43.0 
50.2 
57.3 
64.3 

12.9 
21.0 
28.8 
36.3 
43.7 
50.9 
58.0 
65.0 

Pressure  (Lbs.  per  sq.  ft.) 


0 

104 

144 

190 

243 

303 

10 

.369 

.433 

.511 

.586 

.666 

.762 

.853 

.949 

1.05 

i.16 

20 

1.27 

1.38 

1.50 

1.63 

1.76 

1.90 

2.04 

2.19 

2.34 

2.48 

30 

2.64 

2.81 

2.98 

3.14 

3.32 

3.50 

3.67 

3.87 

4.04 

4.24 

40 

4.44 

4.64 

4.84 

5.07 

5.27 

5.51 

5.72 

5.93 

6.18 

6.40 

50 

6.66 

6.89 

7.12 

7.4 

7.64 

7.88 

8.14 

8.43 

8.69 

8.95 

60 

9.22 

9.49 

9.76 

10.1 

10.4 

10.6 

10.9 

11.2 

11.6 

11.9 

70 

12.2 

12.5 

12.8 

13.1 

13.5 

13.8 

14.1 

14.4 

14.8 

15.1 

80 

15.5 

15.8 

16.2 

16.5 

16.9 

17.3 

17.6 

18.0 

18.4 

18.8 

90 

19.2 

fc   =  maximum  stress  in  concrete  in  Ibs.  per  sq.  in. 
fs    =  maximum  compression  in  steel  in  Ibs.  p;er  sq.  in. 
fs    =  maximum  tension  in  steel  in  Ibs.  per  sq.  in. 
M  =  moment  of  wind  pressure  in  foot  tons.  , 
Then  we  have 


and 


fc  ~  AF 

fs  =  nfc  = 


i-    15 


, (81) 

(82) 

fs=Bfc (83) 

where  A  ana  -B  are  constants  taken  from  the  Tables  LXXXI 
and  LXXXI1. 


394 


REINFORCED    CONCRETE. 


Example. — The  external  diameter  of  a  chimney  is  14.5  ft.,  its 
height  225  ft.,  and  the  thickness  of  the  shell  assumed  to  be  6  ins 
Effective  wind  pressure  is  20  Ibs.  per  sq.  ft. 

Q  =  weight  of  shaft,  approximately  360  tons 

F  =  cross  section  of  shell,  approximately  3150  square  inches 

TABLE  LXXXI. — VALUES  FOR  A  IN  FORMULA  (81). 


R 

A 

r. 

M  =  0 

2.5 

5 

10 

15 

20 

25 

30 

35 

40 

0  5 

0  500 

0.519 

0.538 

0.575 

0.613 

0.650 

0.688 

0.6 

444 

461 

480 

515 

550 

584 

618 

0.7 
0  8 

380 
306 

400 

342 

421 
365 

455 
402 

489 
437 

521 
470 

553 
500 

6  530 

0.9 
1.0 

220 

291 
253 

319 
283 

360 
325 

394 
358 

425 

388 

455 

418 

485 
446 

1.1 
1.2 

223 
199 

254 
230 

297 
273 

328 
303 

357 
331 

385 
358 

413 
384 

0.438 
407 



1.3 
1.4 
1.5 
1.6 
1.8 

!  !! 

180 
163 
150 
138 

211 
195 
181 
170 
151 

253 
235 
219 
206 
184 

282 
264 
247 
233 
209 

309 
290 
272 
257 
231 

334 
313 
295 
279 
251 

358 
336 
317 
300 
270 

381 
358 
338 
320 

289 

6!380 
358 
340 
307 

2  0 

137 

166 

189 

210 

229 

246 

263 

279 

2  2 

151 

173 

193 

210 

225 

241 

256 

2  4 

160 

178 

195 

209 

223 

236 

2  6 

149 

166 

181 

195 

208 

220 

TABLE  LXXXII. — VALUES  FOR  B  IN  FORMULA  (83). 


r. 

M  =  0 

2.5 

5 

10 

15 

20 

25 

30 

35 

40 

0.5 
0  6 

0 

2.5 

0 

2.4 

0 

2.4 

0 

2.3 

0 

2.2 

0 

2.1 

0 
2.0 

0 

0 

0 

0  7 

7  1 

6  2 

5.7 

5  1 

4  6 

4  2 

4  0 

0  8 

17. 

12. 

10. 

8.5 

7.3 

6.7 

6.3 

5.9 

0.9 
1  0 

44. 

19. 
26. 

14.8 
19.6 

11.5 
14.5 

9.9 
12.2 

8.9 
10.9 

8.2 
10. 

7.7 
9.3 

...... 



1.1 

32. 

23.8 

17.1 

14.3 

12.7 

11.6 

10.7 

10.  1 

.2 
.3 

39.5 
45. 

27.5 
30.9 

19.5 
21.6 

16.1 

17.8 

14.2 
15.6 

13. 
14.2 

12. 
13.1 

11.2 
12.3 

4 

50. 

33.8 

23.4 

19.3 

16.9 

15.3 

14.1 

13.3 

12  6 

.5 

54. 

36.5 

25. 

20.6 

18. 

16.3 

15. 

14.2 

13.4 

.6 

g 

57. 

39. 
43  2 

26.6 
29.3 

21.8 
23  7 

19. 
20  7 

17.2 

18  7 

15.8 
17  2 

14.9 
16  2 

14.1 
15  4 

2  0 

47. 

31.8 

25.4 

22.1 

20. 

18.4 

17.3 

16  5 

2  2 

34. 

26  9 

23  3 

21  1 

19  3 

18  2 

17  4 

2  4 

28  2 

24  4 

22  1 

20  2 

19  1- 

18  2 

2  6 

29  3 

25  3 

23 

21  1 

19  8 

18  9 

CHIMNEYS  AND  MISCELLANEOUS  DATA. 


395 


W  —  wind  pressure,  assumed  to  average  14.5  X  200  X  20 

29  tons 

M  -  29  X  100  ft.  =  2900  foot  tons 
AB  -  f-in.    rods    6  ins.  on  centers    -    2?rl4    X    0.4418 

39  sq.  ins. 

1000  As       1000  X   39 
m  =    ~T~  3150 

M  _  2900 
Q    ==   360 
r  -  J  (14.05  —  .05)  =  7  ft. 

Then  we  have,  according  to  Tables  LXXXI  and  LXXXII, 
by  interpolation, 
A  -  0.301 
B  =   15.6 

Q  720000 

hence  f0  =  -^  =  .301  x   3150  "  76     bs>  per  sq>  m 
/•'-   15  X  fe  -  11400  lbs.  per  sq.  in. 
/8  -     /c  -  15.6  X  760  -  11,856  lbs.  per  sq.  in. 
*Approximate     Computation     of     Dimensions.— For    the 
thickness  of  the  steel,  considered  as  a  solid  shell 

/=  — r  X  I  77:7;  |  ,  where  d  =  internal   diameter  in  feet;  wall 
a         \1UU/  j  TT2 

thickness  of  concrete  =  0.1  X  42  Q  Q5H  ^  ~rf~* 

If  we   use   1-in.   round   bars   instead   of  a   steel   ring,   the 
number  of  rods  may  be  found  in  following  table: 
TABLE  LXXXIII. 


H 

100' 

125' 

150' 

175' 

200' 

225' 

250' 

•     No.  of  Rods 

43 

77 

110 

150 

192 

240 

300 

Wall  thickness  for 
H 
d  =  — 

20 

6" 

7" 

8" 

10" 

13" 

15" 

18" 

Summary  of  Points  in  Design  of  Chimneys. — Mr.  San- 
ford  E.  Thompson  sets  forth  the  following  summary  of  es- 
sentials in  design  and  construction  of  a  reinforced  concrete 
chimney.t 

(1)  Design  the  foundations  according  to  the  best  engi- 
neering practice. 

(2)  Compute   the   dimensions   and   reinforcement   in   the 

*From  Heiniche's  Catalog. 

t  Bulletin  American  Portland  Cement  Manufacturers'  Association. 


396  REINFORCED    CONCRETE. 

chimney  with  conservative  units  of  stress,  providing  a  factor 
of  safety  in  the  concrete  of  not  less  than  4  or  5. 

(3)  Provide  enough  vertical  steel  to  take  all  of  the  pull 
without  exceeding  14,000  or,  at  most,  16,000  Ibs.  per  sq.  in. 

(4)  Provide  enough  horizontal  or  circular  steel  to  take 
the  vertical   shear  and  to  resist  the  tendency  to   expansion 
due  to  interior  heat. 

(5)  Distribute    the   horizontal    steel    by   numerous    small 
rods  in  preference  to  larger  rods  spaced  farther  apart 

(6)  Specially   reinforce   sections   where   the   thickness   in 
the  wall  of  chimney  is  changed  or  which  are  liable  to  marked 
changes   of  temperature. 

(7)  Select  first  class  materials  and  thoroughly  test  them 
before  and  during  the  progress  of  the  work. 

(8)  Mix   the    concrete    thoroughly    and   provide    enough 
water  to  produce  a  quaking  concrete. 

(9)  Bond  the  layers  of  concrete  together. 

(10)  Accurately  place   the   steel. 

(11)  Place  the  concrete  around  the  steel  carefully,  ram- 
ming it  so  thoroughly  that  it  will  slush  against  the  steel  and 
adhere  at  every  point. 

(12)  Keep    the    form    rigid. 

The  fulfillment  of  these  requirements  will  increase  the 
cost  of  the  chimney,  but  if  the  recommendations  are  fol- 
lowed there  should  be  no  difficulty  in  erecting  concrete 
chimneys,  which  will  be  very  satisfactory  and  last  forever. 

Construction. — During  the  past  few  years  reinforced  con- 
crete chimneys  have  been  built  in  great  numbers,  both  on 
account  of  their  strength  and  their  cheapness. 

The  construction  is  generally  carried  on  continuously 
from  the  base  to  the  top,  and  the  materials  consist  of 
cement  and  coarse  sand  proportioned  one  to  four. 

Concrete  Chimneys. — Fig.  164  shows  a  chimney  built  for 
the  United  Shoe  Machinery  Co.,  at  Beverly,  Mass.,  and  gives 
the  characteristic  features  of  a  Weber  chimney.  It  is  6  ft. 
in  diameter  and  142  ft.  1  in.  in  height  from  bottom  of  founda- 
tion to  top.  The  foundation  extends  about  16  ft.  below 
ground.  The  shell  is  double  to  the  height  of  48  ft.  above. 


CHIMNEYS  AND  MISCELLANEOUS  DATA.        397 


Plan  of  Foundation. 

Fig.  164. — Chimney  for  United  Shoe  Machinery  Co.,  Beverly,  Mass 


398  REINFORCED    CONCRETE. 

ground,  the  inner  shell  being  4  ins.  thick  and  the  outer  6  ins. 
The  upper  single  shell  portion  is  5  ins.  thick.  The  reinforce- 
ment consists  of  1^x1^x3/16  in.  vertical  and  Ixlx^  in. 
horizontal  T  irons.  The  number  of  bars  in  the  circumference 
and  the  arrangement  of  rods  in  the  foundation  are  given 
in  the  cut. 

Construction  of  Molds. — The  molds  in  the  construction  of 
Weber  chimneys  consist  of  two  rings  of  six  sections,  each 
about  3  ft.  wide  and  connected  by  iron  fastenings.  They  are 
held  in  place  by  friction  on  the  concrete  only  and  are  dis- 
connected before  being  hauled  up  to  the  required  position. 
A  flat  ring  is  located  above  the  forms  to  hold  the  vertical 
steel  bars  in  position  and  alignment  by  running  them  through 
holes  in  the  plate.  This  ring  is  made  of  two  ^4-in.  layers  of 
wood  and  is  pushed  on  ahead  of  the  forms,  also  carrying  the 
beam  for  the  hoisting  pulley.  All  materials  are  hoisted  in- 
side the  chimney.  No  interior  scaffold  is  needed  for  the 
double  shell  and  usually  one  form  a  day  is  filled  and  moved 
up. 

For  the  single  shell,  two  forms  a  day  are  filled.  The 
vertical  bars  lap  24  ins.  where  spliced.  Formerly  a  very  dry 
mix  was  used  and  carefully  tamped,  but  recently  several 
mishaps  have  occurred,  largely  attributed  to  lack  of  water  in 
the  mortar,  so  at  present  a  wetter  mixture  is  being  used. 
The  rings  are  fastened  to  the  vertical  bars  by  means  of  wire 
or  special  clamps.  The  air  space  at  the  bottom  is  connected 
with  the  atmosphere  and  at  the  top  of  the  inner  shell  with 
the  flue  proper.  Care  must  be  taken  to  keep  the  openings  at 
the  bottom  clean  from  waste  concrete  in  order  to  allow  free 
circulation  of  air  around  the  inner  shell. 

The  Wiederholt  Concrete  Steel  Chimney. — The  Wieder- 
holt  chimney  is  built  without  forms  by  the  means  of  thin 
H-shaped  tiles  placed  edge  to  edge  so  as  to  contain  the  con- 
crete and  the  reinforcement. 

Horse-Power  of  Chimneys.— (Kent) 

Let  ^4  =  area  in  sq.  ft.  of  chimney. 

/f=height  in  ft. — H.  P.  =  horse-power. 

then  H.  P.  =3.33  (A-0. 


CHIMNEYS  AND  MISCELLANEOUS  DATA.         399 

MANUFACTURED  ARTICLES. 

Among  the  manufactured  articles  of  reinforced  concrete 
should  be  named  railroad  ties,  fence  posts,  telegraph  poles, 
electric  transmission  poles,  smoke  jacks,  tubs  and  tanks  of 
every  description,  coffins,  roofing  and  siding  plates,  electrier 
conduits,  floor  slabs,  floor  beams,  pile  protection,  stair  steps, 
balusters,  building  blocks,  garden  benches,  manhole  covers, 
chimney  tops,  door  and  window  frames,  sills,  lintels  and 
cornices.  Each  of  these  items  introduces  a  new  field  in  the 
world  of  manufacture,  the  development  of  which  largely  be- 
longs to  the  future  and  the  ingenuity  of  the  concrete  student. 

INSPECTION. 

In  no  other  kind  of  building  construction  is  there  so  much 
need  for  inspection  as  in  reinforced  concrete.  Inspection  of 
the  cement  in  its  manufacture,  after  delivery,  and  on  the  job; 
inspection  of  the  sand  as  to  its  cleanness  and  condition;  in- 
spection of  the  stone  as  to  its  strength  and  size;  inspection 
of  the  mixture  of  the  three  materials  mentioned,  and  inspec- 
tion of  the  amount  of  water  added  to  make  the  proper  con- 
sistency constitute  only  a  small  part  of  what  is  required  of 
an  inspector  on  an  important  reinforced  concrete  construc- 
tion. There  is  the  inspection  of  the  steel  in  the  reinforce- 
ment, the  method  of  making  and  shaping  and  of  assembling 
and  connecting  the  reinforcement,  and,  finally,  of  placing 
and  fastening  it.  There  is  the  inspection  of  the  forms,  the 
quality  of  the  timber,  the  method  of  putting  it  together  to 
meet  the  intention  of  the  designing  engineer,  and  with  a 
view  to  its  easy  removal  so  as  to  be  used  again.  The  filling 
of  forms,  the  spading  and  tamping  of  the  concrete  around 
the  reinforcement  and  against  the  forms  and  the  joining  of 
new  work  to  old  must  be  watched.  An  eye  must  be  kept  on 
the  forms  ahead  of  the  concreting  to  see  that  they  are 
cleaned  free  of  shavings  and  dirt.  While  this  is  going  on  the 
inspector  must  watch  the  action  of  the  forms  and  the  setting 
of  the  cambers,  look  out  for  leaks,  and  at  the  same  time  keep 
an  eye  on  the  contractor's  men  to  see  that  they  do  not  run 
wheel  barrows  or  carry  heavy  loads  over  the  finished  work. 


400  REINFORCED    CONCRETE. 

During  the  hardening,  the  concrete  surface  must  be  kept 
moist.  This  item  is  often  overlooked  in  rush  work. 

After  the  concrete  is  finally  placed,  with  good  materials 
and  mixing  and  good  workmanship,  the  inspector  must  see 
that  the  forms  remain  undisturbed  until  the  concrete  is  hard- 
ened sufficiently  to  enable  the  removal  of  the  struts  and 
braces  keeping  them  in  position.  Too  early  removal  of 
forms  has  been  the  cause  of  most  of  the  deplorable  acci- 
dents which  have  tended  to  retard  the  advancement  of  rein- 
forced concrete  in  the  United  States,  and  which  has  caused 
investors  to  look  askance  at  this  construction,  otherwise  so 
desirable  from  an  engineering  and  economical  standpoint.  It 
is  far  better  to  be  a  few  days  behind  time  than  to  take 
chances  on  a  too  early  removal  of  the  forms.  It  is  also  the 
inspector's  duty  to  see  that  the  naked  concrete  is  protected, 
in  summer  from  the  sun  by  wet  saw  dust  or  wet  blankets 
and  in  the  winter  from  freezing. 

The  cleaning  of  the  molds  is  an  important  item  and 
should  be  well  looked  after  by  the  inspector.  If  the  in- 
spector is  employed  by  the  contractor,  he  should  also  be 
entrusted  with  the  keeping  of  costs,  a  matter  which  will  be 
treated  later. 

PROGRESS  REPORTING  AND   KEEPING  OF  COSTS. 

To  enable  the  engineer  or  contractor  to  estimate  work  in 
a  rational  manner  it  is  absolutely  necessary  for  him  to  note 
down  the  detail  cost  of  the  practical  execution  of  the  work. 
This  will  also  enable  the  contractor  to  analyze  his  expendi- 
tures with  the  view  to  improving  his  foremanship,  laborers, 
plant  equipment,  and  the  like.  By  comparing  his  cost  re- 
ports with  the  different  items  of  his  estimate  he  may  be 
able  either  to  find  leaks  in  his  methods  or  mistakes  in  his 
estimating.  The  cost  of  keeping  progress  and  cost  reports 
is  always  justified  by  the  results.  Several  of  the  best  con- 
struction companies  in  America,  through  a  careful  system  of 
progress  and  cost  reporting,  have  materially  improved  their 


CHIMNEYS  AND  MISCELLANEOUS  DATA.         401 

working  methods   and   their  knowledge   of   the   work   itself, 
besides  securing  data  of  value  for  use  in  future  estimates. 

When  the  manager,  superintendent,  foreman  and  men 
know  that  their  work  is  closely  watched  and  that  not  only 
are  successive  days'  performances  compared  but  that  com- 
parison is  made  with  similar  work  previously  executed  and 
the  result  shown  to  the  credit  or  discredit  of  the  persons  in 
charge  of  the  work,  they  are  spurred  to  do  their  best.  In 
addition  padded  pay  rolls  are  practically  done  away  with,  and 
thefts  of  tools  and  materials  are  reduced  to  a  minimum. 
Machines  are  all  kept  in  better  order,  as  a  falling  off  in  out- 
put is  quickly  discovered,  and  it  is  a  fact  that  the  contractor 
who  has  a  reputation  of  having  a  good  system  of  watching 
the  cost  of  his  work  is  more  apt  to  be  trusted  with  per- 
centage work  or  actual  cost  plus  a  fixed  sum  for  his  super- 
vision and  the  use  of  his  plant.  To  the  engineer  in  charge 
of  the  work  such  reporting  is  of  incalculable  value,  and  he 
will  soon  find  in  Gillette's  words  that  "it  is  fatal  to  good  en- 
gineering to  copy  a  specification  without  weighing  the  dol- 
lars and  cents  effect  of  every  word  and  phrase.  He  will  see 
that  there  is  more  than  strains  and  stresses  in  the  design  of 
a  bridge  and  more  than  coefficients  of  friction  in  conduits 
and  canals."  The  labor  items  in  reinforced  concrete  of 
which  costs  are  to  be  recorded  generally  are  as  follows: 

(1)  Stone  crushing. 

(2)  Concrete  mixing  and  spreading. 

(3)  Making  and  placing  reinforcement. 

(4)  Making  and  placing  forms,  including  removal  of  same. 

(5)  Finishing. 

For  each  of  these  items  the  author  prefers  to  use  a  card 
to  be  filled  out  daily  in  duplicate  by  using  a  carbon  sheet,  the 
original  being  sent  to  the  office  to  be  entered  on  the  weekly 
report  by  a  person  kept  in  the  office  for  this  particular  pur- 
pose, and  the  copy  to  remain  at  the  job.  The  weekly  report 
should  be  made  in  a  form  comparable  with  the  estimate  form 
and  in  such  a  shape  that  at  any  time  the  total  cost  of  labor 


402 


REINFORCED    CONCRETE. 


to  date  can  be  added  up  for  each  item.  The  daily  report 
cards  should  be  numbered  and  dated  and  show  remarks  re- 
ferring to  such  materials  or  other  items  as  will  be  directly 
needed  to  prevent  any  stoppage  or  delay  of  the  work  so  that 
the  office  is  constantly  kept  informed  as  to  proper  delivery 
of  material.  A  copy  of  all  contracts  with  all  conditions  for 
delivery  of  tools  or  materials  should  be  on  hand  at  the  con- 
struction office  on  the  job  so  the  superintendent  may  know 
exactly  how  to  act  without  being  compelled  to  await  in- 
structions from  the  office  in  case  he  sees  he  will  run  short  of 
material.  All  orders  issued  from  the  office  or  from  the  job 
should  be  in  triplicate,  one  for  the  party  furnishing  mate- 
rials, one  for  the  office  or  the  job  as  the  case  may  be,  and 
one  for  file.  It  will  be  found  convenient  to  make  these  re- 
port cards  suitable  for  an  index  card  file,  hence  of  fairly 
stiff  paper,  the  ones  sent  to  the  office  being  perforated  and 
torn  out  of  the  book  and  those  on  the  job  to  remain  in  the 
book.  Sample  cards  as  used  by  the  author  are  shown  herewith. 


Contract  No. 


BLASTING. 


New  York 19... 


No.  of  Bias 
No.  of  houi 
Remarks 

ts  

Foreman 
Engineer 
Firemen 

Derrick 
Lahore 
Coal.  .  . 

men 

;                 .... 

rs  .  .  .  .            .... 

Rockmen 
Drillers.  . 

Repair; 
Sundrie 

;  



;S  

Total 

Pay 
rolls. 

Hauled 
to 
crushers 

Hauled 
to 
dump. 

Used 
in 
walls. 

Blasted 
cu.  yds. 

Feet 
drilled. 

Average 
cost 
ru.  yd. 

Cost 

hauling. 

Previous.  . 
To-day 

Total 

Clerk 


Supt. 


CHIMNEYS  AND  MISCELLANEOUS  DATA.        403 


REINFORCED  CONCRETE 
FORMS. 


' 

Where  workini 

j 

Foreman 

Carpenters 

Remarks.  .  . 

Laborers  

Lathers  

Sundries 

Sq.  ft. 
slabs. 

Lin.  ft. 
beams. 

Lin.  ft. 
col's. 

Pay         Feet          Old           New 
roll.        B.  M.        stuff.       material. 

Previous 

To-day 

Total 

Clerk 

Siint 

Contract  No 

CRU 

SHING. 

New  York  19. 

Teams  to  "A"  Street 
Teams  to  "B"  Street 
Remarks 

$ 

Foreman             .                                        .  . 

$ 

Engineers       

Laborers      ....          .  . 

Repairs    

Lumber  

Delivered 
to  "A"  St. 

Delivered 
to  "B"  St. 

Hauling. 

crushers.      Pay  roll     Pay  roll  crushing. 
"A"  St.     "B"  St. 

To-dav 

On  hand 

Total 

Clerk . 


Supt. 


404 


Contract  No. 


REINFORCED    CONCRETE. 

MASONRY. 


New  York ..19. 


Where  working. 


Remarks. 


Foreman. 
Masons. . 
Laborers. 
Sundries. 


Pay 

rolls. 

Bbls. 

cement. 

Bbls. 

lime. 

Yards 
sand. 

Yards 
rock. 

Yards 

Masonry. 

Average 
cost  per 
yard. 

Previous.  .  . 

To-day..  .  . 

Total  

Clerk 


Supt. 


SAND. 


Contract  No. 


New  York, . ., 


.19. 


Remarks. 

Wagon  loads 
received  from 

Cubic  yards 
received. 

Cubic  yards 
used  masonry. 

Cubic  yards 
used  brickwork. 

Cubic  yards 
used  concrete. 

ibic  yards 
ed  reinforced 
ncrete. 

o38 

Today 

Total 

Clerk 


Supt. 


CHIMNEYS  AND  MISCELLANEOUS  DATA.         405 
CEMENT. 


Contract  No. 


New  York 19... 


Receivec 

I. 

Ba 

gs. 

1 

d 

. 

Remarks. 

Car 

numbers. 

No. 
bbls. 

•d 

•o 

«S 

•g* 

o  -^ 

5 

X 

* 

1 

> 

c 

§ 

g£ 

C  u 

a 

^0 

1 

$ 

1 

rt 

1 

3 

« 

l^ 

« 

t> 

To-day 

, 

Total 

- 

Clerk , 


Supt. 


NOTES  ON  ESTIMATING.* 

In  estimating  unit  prices,  too  much  reliance  should  not  be 
placed  on  the  published  prices  for  similar  work.  Conditions 
vary  greatly  in  places  but  a  short  distance  apart;  thus  wages 
may  be  different,  engineers  may  have  entirely  different  in- 
terpretations of  identical  specifications,  and  bidding  prices 
as  published  may  be  perfectly  unbalanced,  being  too  high 
on  certain  items  with  a  view  of  getting  the  money  out  of  the 
job  at  once,  and  too  low  on  others.  It  must  be  remembered 
that  a  unit  price  that  is  fair  for  a  large  job  is  generally  too 
low  for  a  small  job,  and  furthermore  a  contractor  already 
equipped  with  a  plant  can  often  afford  to  bid  lower  than 
contractors  who  may  be  compelled  to  buy  a  new  plant.  For 
this  reason  each  item  should  be  estimated  in  detail  and  as  a 
rule  may  be  considered  under  the  following  heads: 


*Summarized  from   Gillette's   "Handbook  of  Cost  Data." 


406  REINFORCED    CONCRETE. 

(1)  Plant  expenses  and  supplies. 

(2)  Materials. 

(3)  Labor. 

(4)  Superintendence  and  general  expense. 

The  plant  expense  includes  interest  and  depreciation  on 
all  tools,  machines,  buildings,  store  materials,  trestles,  false 
work,  and  also  cost  of  maintaining  the  plant  during  its 
operation,  new  parts,  fuel,  oil,  etc.  Materials  include  only 
such  materials  as  actually  go  into  the  finished  structure  and 
the  waste  of  materials  due  to  breakage  in  handling  or  saw- 
ing and  shaping.  The  cost  of  materials  also  includes  the 
freight  and  the  hauling  to  the  site  of  the  work.  Labor  in- 
cludes all  skilled  and  common  labor  including  foreman  and 
time  Leeper,  but  excluding  superintendent  and  office  expense. 

Superintendence  and  general  expense  include  all  general 
office  expenses  which  are  to  be  divided  on  all  jobs,  such  as 
rents,  taxes,  telephones,  traveling  and  entertaining  expenses, 
stationery,  etc. 

Plant  Expense. — In  estimating  the  cost  of  a  plant  it  must 
be  based  upon  a  time  limit  at  least  20  per  cent  less  than  the 
one  mentioned  in  the  contract,  in  addition  to  liberal  allow- 
ances for  bad  weather,  delivery  delays  and  break  downs. 
Use  with  great  caution  the  figures  of  output  given  in  cata- 
logs; they  are  almost  invariably  based  upon  ideal  conditions 
and  frequently  wholly  deceptive. 

For  example,  while  a  derrick  may  be  able  to  handle  200 
cu.  yds.  a  day,  in  a  confined  space  its  actual  output  may  not 
exceed  30  cu.  yds.  Do  not  guess  at  anything;  if  you  have 
no  other  data  secure  some  estimates  of  output  of  a  similar 
plant  from  large  and  old  manufacturing  firms  and  compare 
their  statements.  Having  liberally  estimated  the  size  and 
kind  of  plant  required,  charge  the  full  cost  of  the  plant  up 
to  the  job  to  be  done  and  determine  how  many  cents  per 


CHIMNEYS  AND  MISCELLANEOUS  DATA.        407 

yard  or  other  units  involved,  are  thus  chargeable  to  the  first 
cost  of  plant.  This  will  give  a  maximum  charge,  and  it  is 
well  to  know  the  worst;  but  if  the  full  cost  of  a  plant  is 
charged  to  a  small  job  some  other  contractor  will  probably 
get  the  work.  Go  therefore  to  a  dealer  in  second-hand  ma- 
chinery and  ask  him  to  name  a  fair  price  on  a  second-hand 
plant  such  as  yours  will  be,  when  you  are  through  with  it. 

If  you  can  secure  a  tentative  bid  on  the  machinery,  you 
will  have  a  fairly  reliable  estimate  of  its  salvage  value.  A 
plant  can  also  be  rented  at  so  much  a  day  or  a  month,  and 
for  short  jobs  this  is  usually  the  best  policy,  inasmuch  as  it 
never  pays  a  contractor  to  be  encumbered  with  much  ma- 
chinery, etc.  Depreciation  of  a  plant  should  include  all  the 
cost  of  housing  and  caring  for  the  same,  and  be  distributed 
over  the  average  number  of  days  that  the  plant  is  actually 
worked. 

Current  repairs  cannot  always  be  separated  from  depre- 
ciation and  it  is  well  to  consider  the  replacing  of  all  parts 
that  wear  out  rapidly  as  being  current  repairs.  Of  course 
depreciation  is  a  variable  item;  thus  a  cable-way,  for  exam- 
ple, may  last  two  years  if  it  handles  only  2S,000  skip-loads 
per  year,  but  if  100,000  loads  are  handled  in  a  year  two  cables 
will  be  worn  out. 

In  figuring  cost  of  fuel  for  engines,  it  is  customary  to 
allow  one-third  of  a  ton  of  coal  for  each  10  H.  P.  per  10- 
hour  shift. 

General  expenses  on  contracts  of  $100,000  or  more  run 
about  2>}/2  per  cent,  and  under  $100,000  from  4  per  cent  up. 
The  author  has  for  many  years  used  3  per  cent  and  found 
that  it  averaged  just  about  right. 

Percentage  to  Allow  for  Profits. — This  is  a  question  which 
has  been  much  discussed.  The  percentage  should  depend 
upon  the  ratio  between  materials  and  labor  employed  and  the 
duration  of  the  contract,  as  well  as  its  size.  A  percentage 


408  REINFORCED    CONCRETE. 

of  10  for  material  and  20  to  25  on  labor,  where  the  material 
is  furnished  by  some  one  else,  is  fair  and  customary.  In 
addition  to  the  percentage  for  profit  there  should  be  added  a 
small  percentage,  say  2  or  3  per  cent,  for  contingencies. 

Accident  Insurance. — The  following  is  taken  from  a  lec- 
ture to  the  students  of  engineering  of  Columbia  University 
by  Mr.  Gillette: 

"Never  omit  an  allowance  for  accidents  and  other  unfore- 
seen contingencies.  Second,  never  neglect  to  insure  the 
workmen. 

"A  blanket  policy  covering  all  the  men  can  be  taken  out. 
The  premium  is  a  given  percentage  of  the  pay  roll.  This  in- 
surance does  not  give  to  each  man  a  weekly  stipend  in  case 
of  accident  or  to  his  heirs  a  designated  sum  in  case  of  death. 
But  what  the  insurance  company  does  do  is  to  protect  a  con- 
tractor by  assuming  all  liabilities  from  claims  made  by  in- 
sured workmen  or  their  heirs.  The  insurance  company  lim- 
its this  liability,  however,  so  that  in  case  a  number  of  men 
are  killed  by  one  accident  the  contractor  may  have  to  stand 
part  of  the  damages.  No  matter  how  safe  the  work  seems 
to  be,  a  contractor  should  never  neglect  to  take  out  a  pay 
roll  insurance  policy.  Many  a  contractor  just  starting  in 
business  has  been  ruined  through  failure  to  insure  against 
accident." 

In  making  estimates  of  any  structure  the  first  step 
should  be  to  make  a  list  of  all  the  items  which  possibly 
may  come  into  consideration,  and  the  engineer  or  contractor 
should  look  over  this  list  for  every  estimate  he  makes  and 
check  off  such  items  as  they  have  been  covered.  Such  list  of 
items  should  also  be  prepared  and  completed  from  the  speci- 
fications, every  item  in  the  specification  being  represented 
on  the  estimating  sheet.  A  sample  estimate  is  here  added 
for  the  guidance  of  an  engineer  or  contractor  on  similar 
work. 


CHIMNEYS  AND  MISCELLANEOUS  DATA.        409 


BLANK  FORM  FOR  ESTIMATE  OP  BUILDING. 


Excavation. 

Wrecking. 
Blasting. 
Sheeting. 
Excavating. 

Piling. 

White  oak   piling. 
Mixed   piling. 
Snubbing*  piles. 
Concrete   piles. 

Caissons. 

Lumber. 

Rings. 

Excavating. 

Dampproofing. 
Masonry. 

Plain   concrete. 
Dimension   stone. 
Rubble  work. 

Granite. 

Carving. 
Lewising. 
Cartage. 
Setting. 
Cut  Stone. 

Exterior   marble. 

Carving. 

Lewising. 

Cartage. 

Setting. 

Blue    Stone. 

Sills  and  lintels. 
Copings. 
Walks. 
Curbs. 
Cartage. 
Setting. 
Terra  Cotta. 
Cartage. 
Setting. 

Brickwork. 

Common  brick. 
Pressed    brick. 
Glazed  brick. 
Hollow  brick. 

Plastering. 
Lathing. 

Suspended  ceilings. 
Corner    beads. 
Patching. 


Reinforced   Concrete. 

Forms. 

Concrete. 

Reinforcement. 

Finishing. 

Cement    floors. 

Marble. 

Mosaic  and  tile. 

Scagliola. 

Terrazzo. 

Concrete  base  for  same, 

Fire    Proofing. 

Hollow   tile. 

Book    tile. 

Iron  fittings  or  rods. 

Patching. 

Structural    Steel   and    Iron. 

Castings. 

Cartage. 

Setting. 

Inspection. 

Shop    drawings. 

Painting. 

Chimney. 

Ornamental   Iron. 

Stairways. 

Railings. 

Elevator  enclosures. 

Bronze. 

Prismatic   lights. 

Stair   treads. 

Hardware. 

Nails. 

Screws. 

Bolts. 

Ladders    and    fire    escapes. 

Straps. 

Gratings. 

Hinges. 

Plumbing. 

Gas   fitting. 
Electric  Wiring. 

Bells. 

Speaking   tubes. 
Telephones. 
Watchman's   clocks. 
Electric    fixtures. 
Lamps. 
Pneumatic   tubes. 


410 


REINFORCED    CONCRETE. 


Mail    Chute. 
Power    Plant. 

Boilers. 

Boiler    setting. 
Engines. 
Foundations. 
Dynamos. 
Switchboards,    etc. 
Feed  pump. 
Fire  pump. 
Steam  piping. 
Water   intake. 
Water   piping. 
Condenser. 
Hot   well. 

Sprinkler   System. 
Dust    Collecting. 
Heating. 

Ventilating. 
Elevators. 

Passenger   elevators. 
Freight    elevators. 
Sidewalk  lifts. 
Dumbwaiters. 
Signal  device. 
Esculators. 

Drawn  Metal    Covered  WorK. 

Metal   frames. 
Tin    doors. 
Shutters. 
Sheet  Metal  and   Roofing. 

Corrugated   iron  covering. 

Flashings. 

Cornices. 

Gutters. 


Downpipes. 
Skylights. 
Roof   covering. 

Carpentry. 

Rough   carpentry. 
Finishing   work. 
Closet  work. 

Ml  II  work. 

Frames. 

Sash. 

Trim. 

Filling. 

Priming. 

Glass. 

Leaded  glass. 
Screen   prisms. 
Plate    glass. 
Common  glass. 
Glazing. 

Painting. 

Varnishing. 

Tinting. 

Paper  hanging. 

General    Expenses. 

Tools  and  tackles. 

Freight   on    same. 

Traveling  expense. 

Liability    insurance. 

Fire   insurance. 

Storehouse  and  office  sheds. 

Salvage. 

Depreciation. 

Office    expenses. 

Inspection. 

Winding  up. 


To  these  items  are  added  in  grain  elevator  construction; 


Sheet  Iron   Linings. 
Garners. 
Scales. 

Receiving  hoppers. 
Shipping   bins. 
Elevator    heads. 
Spouting. 

Machinery. 

Power   transmission   complete. 

Scales. 

Steam   shovels. 

Car  pullers. 

Elevator  legs. 

Cleaner  legs. 


Belting. 

Erection   of  machinery. 

Elevator   house    castings. 

Elevator  boot   tanks. 

Conveyors. 

Framing  for  conveyors 
R.    R.   Track   Doors. 
Portable    Spouts. 
Scale    Spouts. 
Stand  Pipes. 

Hoods    Over    Loading    Spouts. 
Painting     Name. 

Lettering  house  inside. 


SPEC  I  PICA  TIONS.  41 1 

GENERAL      SPECIFICATIONS      FOR      REINFORCED 
CONCRETE. 

In  General. — Special  attention  must  be  given  to  the 
quality  of  materials,  labor  and  character  of  workmanship 
and  these  specifications  are  intended  to  include  all  that  is 
considered  best  in  theory  and  practice. 

Only  persons  or  firms  thoroughly  experienced  in  this 
class  of  work  will  be  considered  as  bidders. 

Bidders  must  submit  drawings  indicating  their  method  of 
construction  and  calculation;  the  arrangement  and  nature  of 
their  steel  reinforcement  must  be  plainly  stated  and  must 
have  been  approved  by  the  building  departments  of  such 
of  the  principal  cities  in  the  United  States  as  have  studied 
reinforced  concrete  and  have  embodied  conditions  for  gov- 
erning its  use  in  their  building  codes,  such  as  New  York, 
Brooklyn,  Minneapolis,  St.  Louis,  Philadelphia,  Washington, 
Cleveland,  San  Francisco  and  Chicago. 

Dimensions  of  beams,  columns,  slabs  and  other  parts  of 
the  construction  indicated  on  the  drawings  shall  be  con- 
sidered a  minimum. 

Samples  of  all  materials  must  be  submitted  to  the  en- 
gineer for  approval  before  being  used  and  all  rejected  mate- 
rials must  immediately  be  removed  from  the  building,  if  re- 
quested by  the  engineer. 

No  bids  will  be  considered  without  submission  to  these 
conditions. 

In    calculations    beams   and    slabs    continuous   over   their 

supports  may  be  computed  for  a  bending  moment  of  ~-rx 
and  slabs  continuous  over  supports  on  four  sides  may  be 

pr- 

computed   for    a    bending    moment  -^ft-      In    all    such    cases 

sufficient  reinforcement  must  be  provided  at  the  top  of  the 
slab  to  take  care  of  all  regular  bending  moments  at  the  sup- 
ports. 


412  REINFORCED    CONCRETE. 

Particular  attention  must  be  given  to  the  compression  on 
under  side  of  beams,  where  four  beams  or  girders  meet  in  a 
column. 

Cement. — Standard  specifications  adopted  by  American 
Society  for  Testing  Materials  (see  page  3) : 

The  contractor  shall  notify  the  engineer  as  soon  as  each 
car  of  cement  is  placed,  so  samples  may  be  taken  therefrom 
without  delay. 

The  cement  shall  be  stored  in  a  suitable  weatherproof 
building  having  the  floor  blocked  up  from  the  ground  and  in 
a  manner  easy  of  access,  and  proper  inspection  and  identifi- 
cation of  each  carload.  Fourteen  days  at  least  shall  be 
allowed  for  inspection  and  tests.  The  name  and  brand  of 
manufacturer  shall  be  on  each  bag. 

Cement  failing  in  the  seven  day  requirement  may  be 
held  awaiting  the  results  of  the  28  days'  test  before  rejec- 
tion. 

Sand. — Shall  be  coarse,  sharp,  clean,  a  combination  of 
coarse  and  fine,  approximately  3  parts  of  coarse  to  1  part  of 
fine  as  hereinafter  described.  All  sand  shall  pass  through  a 
screen  of  5  rneshes  to  the  linear  inch,  approximately  75%  of 
above  shall  be  rejected  by  a  screen  of  12  meshes  to  the  inch; 
the  other  quarter  shall  be  fine  sand.  Salt  water  beach  sand 
shall  be  washed,  and  any  sand  containing  more  than  3% 
loam  or  other  impurities  shall  be  rejected. 

Gravel  or  Stone. — Gravel  shall  pass  through  a  2^-in. 
mesh  and  be  rejected  by  a  ^-in.  mesh.  If  salt  water  gravel 
is  used  it  shall  be  washed  clean  the  day  previous  to  incor- 
poration in  the  concrete.  Stone  shall  be  hard  granite,  trap 
rock  or  limestone,  and  crushed  to  pass  a  %-in  ring,  while  re- 
jected on  a  J4~m-  ring. 

Proportion. — The  mixture  shall  be  1  volume  of  Portland 
cement  as  specified  to  6  volumes  of  aggregates,  whose  re- 
spective quantities  will  give  a  maximum  density. 

To  determine  the  minimum  volume  differently  propor- 
tioned mixtures  shall  be  placed  in  a  vessel  (say  a  piece  of 


SPECIFIC  A  TIONS.  413 

wrought  iron  pipe  9  ins.  diameter  by  12  ins.  high)  and  mixed 
and  stirred  with  water  until  the  proportion  is  found,  which 
for  the  same  combined  weight  gives  the  minimum  volume. 

Mixing. — Shall  be  done  by  batch  mixer,  the  mixing  being 
continued  at  least  3  minutes  to  each  batch,  resulting  in  a 
uniform,  evenly  tempered  concrete.  Enough  water  shall  be 
added  to  result  in  a  small  quantity  of  free  mortar  appearing 
on  top  of  the  concrete  under  tamping.  A  competent  fore- 
man or  inspector  must  at  all  times  be  watching  the  mate- 
rial going  into  the  mixer,  as  well  as  the  concrete  coming  out. 

Placing  Concrete. — Concrete  shall  be  placed  as  rapidly  as 
possible  after  leaving  the  mixer  and  shall  at  once  be  thor- 
oughly puddled,  spaded  and  tamped.  Any  concrete  not  placed 
after  it  is  H  hour  old  shall  be  thrown  away. 

Concreting  when  started  shall  be  vigorously  carried  on  to 
completion.  If  concreting  is  stopped  before  an  entire  floor 
is  completed  the  stop  shall  be  made  in  the  center  of  the 
beams  and  center  of  floor  slabs.  The  plane  where  concrete 
work  is  stopped  must  be  at  right  angles  to  the  direction  of 
the  beam  or  slab.  In  no  event  shall  work  be  terminated  in 
beams  or  floor  slabs  where  future  shearing  action  becomes 
great,  as  at  their  ends  or  directly  under  a  heavy  concentrated 
load.  Before  work  is  resumed,  the  old  work  shall  be  thor- 
oughly sprinkled  with  water  and  pure  cement  strewn  over 
the  joint  to  be  abutted. 

Wet  all  forms  just  before  concreting. 

Reinforcement. — Reinforcing  steel  shall  be  so  arranged, 
designed  and  manufactured  that  it  cannot  be  misplaced  in  the 
forms,  and  that  it  of  itself  maintains  the  proper  distance 
from  bottom  and  side  of  forms.  It  shall  be  calculated  to 
provide  for  all  horizontal  and  diagonal  tension,  vertical 
shear  and  compression  where  there  is  not  sufficient  concrete 
for  the  purpose.  Concrete  shall  not  be  charged  with  more 
than  75  Ibs.  per  sq.  in.  for  shearing  stress.  No  steel  shall  be 
closer  to  the  form  than  Y±  in. 

Steel  rods  shall  have  an  elastic  limit  not  to  exceed  50,000 
Ibs.  Wire  in  fabric  shall  have  an  elastic  limit  of  80,000  Ibs. 


414  REINFORCED    CONCRETE. 

or  more.  No  iron  shall  be  painted.  A  slight  film  of  rust  is 
not  objectionable,  but  no  scale  will  be  permitted.  All  rods 
shall  have  ends  bent  1  in.  up  at  90°.  All  steel  shall  bend  cold 
180°  around  its  own  diameter  without  cracking. 

All  reinforcement  shall  be  anchored  to  its  surroundings, 
structural  steel,  brick  work,  or  masonry,  and  if  rods  are 
spliced  they  shall  overlap  each  other  at  least  40  diameters 
for  steel  rods  and  50  diameters  for  wire. 

Expansion. — Expansion  and  contraction  from  temperature 
changes  or  other  causes  shall  be  taken  up  by  distributing 
rods  in  slabs  and  walls,  preferably  in  the  shape  of  a  wire 
fabric  of  high  tensile  strength  wire. 

Centering. — All  centering  must  be  true,  rigid  and  prop- 
erly braced,  and  able  to  carry  the  dead  loads,  including 
weight  of  construction  considered  as  a  liquid,  without  deflec- 
tion. Forms  are  to  be  bolted  and  all  slab  forms  arranged  to  be 
given  a  camber,  so  as  to  leave  the  slab  perfectly  horizontal  after 
setting.  If  the  reinforced  concrete  rests  on  structural  steel  or 
part  of  the  reinforcement  consists  of  structural  steel,  the  forms 
shall  be  suspended  from  said  steel,  so  that  the  latter  may  obtain 
its  deflection  or  initial  stresses  due  to  the  dead  loads  while  the 
concrete  is  setting. 

Removal  of  Forms. — Centering  must  not  be  removed  un- 
til the  concrete  has  thoroughly  set  and  not  until  permission 
has  been  obtained  from  the  engineer. 

Beams  shall  remain  supported  for  at  least  two  weeks 
after  all  other  false  work  has  been  removed.  Columns  shall  not 
be  given  their  full  load  in  less  than  five  weeks  after  concret- 
ing. 

Freezing  Weather. — Concrete  shall  be  placed  in  freezing 
weather  only  when  it  cannot  possibly  be  avoided.  Precau- 
tion shall  be  taken  to  protect  the  finished  work.  Forms  for 
such  work  shall  be  left  in  place  at  least  three  weeks  longer 
than  customary. 

Protecting  Work. — All  floors  shalf  be  covered  with  saw- 
dust and  sprinkled  for  four  days  after  concreting,  and  'all 


SPECIFICATIONS.  415 

work  exposed  to  the  weather  shall  be  kept  moist  by  sprink- 
lin'g  or  wet  canvas  for  at  least  one  week. 

Fireproofing  Structural  Steel. — All  structural  steel  shall 
be  protected  by  1:2^  mortar  plastered  on  a  wire  fabric, 
such  plastering  being  ll/2  ins.  thick. 

Cement  Finish. — Cement  finish  for  floors  shall  not  be 
leaner  than  1:2,  using  in  all  cases  a  specially  sharp,  clean 
and  gritty  sand.  It  shall  be  troweled  to  a  thoroughly  smooth 
and  even  surface  and  be  cut  in  squares  not  less  than  8  ft. 
square. 

Cement  finish  when  applied  to  a  concrete  base  must  be 
laid  at  the  same  time  as  the  concrete  and  shall  not  be  less 
than  l/2  in.  thick. 

Stresses. — For  hooped  columns  750  Ibs.  per  sq.  in. 

For  latticed  columns,  500  Ibs-.  per  sq.  in. 

For  shearing  stresses  in  concrete,  75  Ibs.  per  sq.  in. 

For  shearing  stresses  in  steel,  10,000  Ibs.  per  sq.  in. 

For  tension  stresses  in  steel,  l/2  of  the  elastic  limit. 

For  tension  stresses  in  wire,  l/3  of  the  elastic  limit. 

Extreme  fiber  stress  in  slabs,  800  Ibs.  per  sq.  in. 

Extreme  fiber  stress  in  beams  and  girders,  750  Ibs.  per  sq. 
in. 

Ratio  of  moduli  of  elasticity  of  concrete  and  steel,  1  to  20. 

The  tensile  strength  of  concrete  shall  not  be  considered. 

Tests. — Floors  shall  be  tested  one  month  after  the  cen- 
tering has  been  removed,  to  a  uniformly  distributed  load 
equal  to  twice  the  safe  live  load.  With  this  load  there  shall 
not  be  a  deflection  exceeding  1/400  of  the  span,  and  the 
floor  shall  return  to  its  normal  position  after  the  removal  of 
the  load. 

Finally. — At  such  time  as  the  engineer  directs  and  finally 
upon  completion  of  the  work  the  contractor  shall  remove 
all  rubbish  and  surplus  materials  and  repair  such  damage  as 
may  have  been  done  to  the  work  by  other  contractors  in 
the  course  of  ordinary  building  construction,  and  shall  leave 
the  premises  in  a  neat,  clean  and  perfect  condition  acceptable 
to  the  engineer. 


416  REINFORCED    CONCRETE. 

STANDARD     SPECIFICATIONS     FOR     CEMENT     OF 

THE  AMERICAN  SOCIETY  FOR  TEST- 

ING  MATERIALS. 

(1)  All  cement  shall  be  inspected. 

(2)  Cement  may  be  inspected  either  at  the  place  of  manu- 
facture or  on  the  work. 

(3)  In  order  to  allow  ample  time  for  inspecting  and  test- 
ing, the  cement  should  be  stored  in  a  suitable  weather-tight 
building   having  the   floor  properly   blocked   or   raised   from 
the  ground. 

(4)  The  cement  shall  be  stored  in  such  a  manner  as  to 
permit  easy  access  for  proper  inspection  and  identification  of 
each  shipment. 

(5)  Every  facility  shall  be  provided  by  the  contractor  and 
a  period  of  at  least  twelve  days  allowed  for  the  inspection 
and  necessary  tests. 

(6)  Cement  shall  be  delivered  in  suitable  packages  with 
the  brand  and  name  of  manufacturer  plainly  marked  thereon. 

(7)  A  bag  of  cement  shall  contain  94  pounds  of  cement 
net.     Each  barrel  of  Portland  cement  shall  contain  4  bags, 
and  each  barrel  of  natural  cement  shall  contain  3  bags  of  the 
above  net  weight. 

(8)  Cement  failing  to  meet  the  seven-day  requirements 
may  be   held   awaiting   the   results   of  the   twenty-eight  day 
tests  before  rejection. 

(9)  All    tests    shall    be    made    in    accordance    with    the 
methods  proposed  by  the  Committee  on  Uniform  Tests  of 
Cement   of   the   American    Society   of   Civil    Engineers,   pre- 
sented to  the  society  January  21,  1903,  and  amended  Janu- 
ary 20,  1904,  with  all  subsequent  amendments  thereto. 

(10)  The  acceptance  or  rejection  shall  be  based  on  the 
following  requirements: 

(11)  Natural  Cement. — Definition:     This  term  shall  be  ap- 
plied to  the  finely  pulverized  product  resulting  from  the  cal- 
cination of  an  argillaceous  limestone  at  a  temperature  only 
sufficient  to  drive  off  the  carbonic  acid  gas. 


SPECIFICATIONS.  417 

(12)  The  specific  gravity  of  the  cement  thoroughly  dried 
at   100°   C.   shall   be  not  less   than  2.8. 

(13)  Fineness. — It  shall  leave  by  weight  a  residue  of  not 
more  than  W%  on  the  No.  100  and  30%  on  the  No.  200  sieve. 

(14)  Time  of  Setting. — It  shall  develop  initial  set  in  not 
less  than  ten  minutes  and  hard  set  in  not  less  than  thirty 
minutes,  nor  more  than  three  hours. 

(15)  Tensile   Strength. — The   minimum   requirements   for 
tensile  strength  for  briquettes  1  in.  square  in  cross  section 
shall    be    within    the    following   limits,    and    shall    show   no 
retrogression  in  strength  within  the  periods  specified: 

(For  example>  the  minimum  requirement  for  the  twenty- 
four  hour  neat  cement  test  should  be  some  value  within  the 
limits  of  50  and  100  pounds,  and  so  on  for  each  period 
stated.) 

Age.                Neat  Cement.  Strength. 

24  hours  in  moist  air ' 50-100  Ibs. 

7  days  (1  day  in  moist  air,  6  days  in  water) 100-200  Ibs. 

28  days  (1  day  in  moist  air,  27  days  in  water)..  ..200-300  Ibs. 
One  part  cement,  three  parts  standard  sand — 

7  days  (1  day  in  moist  air,  6  days  in  water) 25-75    Ibs. 

28  days  (1  day  in  moist  air,  27  days  in  water) 75-150  Ibs. 

(16)  Constancy  of  Volume. — Pats   of  neat  cement  about 
3  ins.  in  diameter,  ^  in.  thick  at  center,  tapering  to  a  thin 
edge,  shall  be  kept  in  moist  air  for  a  period  of  twenty-four 
hours. 

(a)  A  pat  is  then  kept  in  air  at  normal  temperature. 

(b)  Another  is  kept  in  water  maintained  as  near  70°  F.  as 
practicable. 

(17)  These  pats  are  observed  at  intervals  for  at  least  28 
days,  and,  to  satisfactorily  pass  the  tests,  should  remain  firm 
and  hard  and  show  no  signs  of  distortion,  checking,  cracking, 
or  disintegrating. 

(18)  Portland  Cement. — Definition:     This  term  is  applied 
to  the  finely  pulverized  product  resulting  from  the  calcina- 
tion to  incipient  fusion  of  an  intimate  mixture  of  properly 
proportioned   argillaceous   and   calcareous   materials,   and   to 


418  REINFORCED    CONCRETE. 

which   no   addition   greater   than  3%  has  been   made   subse- 
quent to  calcination. 

(19)  Specific  Gravity. — The  specific  gravity  of  the  cement, 
thoroughly  dried  at  100°  C,  shall  not  be  less  than  3.10. 

(20)  Fineness. — It  shall  leave  by  weight  a  residue  of  not 
more  than  8%  on  the  No.  100  and  not  more  than  25%  on  the 
No.  200  sieve. 

(21)  Time  of  Setting.— It  shall  develop  initial  set  in  not 
less  than  thirty  minutes,  but  must  develop  hard  set  in  not 
less  than  one  hour,  nor  more  than  ten  hours. 

(22)  Tensile   Strength. — The   minimum   requirements   for 
tensile  strength  for  briquettes  1  in.  square  in  section  shall  be 
within  the  following  limits,  and  shall  show  no  retrogression 
in  strength  within  the  periods  specified. 

(For  example,  the  minimum  requirement  for  the  twenty- 
four  hour  neat  cement  test  should  be  some  value  within  the 
limits  of  150  and  200  pounds  and  so  on  for  each  period 
stated.) 

Age.                Neat  Cement.  Strength. 

24  hours  in  moist  air 150-200  Ibs. 

7  days  (1  day  in  moist  air,  6  days  in  water) 450-550  Ibs. 

28  days  (1  day  in  moist  air,  27  days  in  water)..  ..550-650  Ibs. 
One  part  cement,  three  parts  sand — 

7  days  (1  day  in  moist  air,  6  days  in  water) 150-200  Ibs. 

28  days  (1  day  in  moist  air,  27  days  in  water) 200-300  Ibs. 

(23)  Constancy  of  Volume. — Pats  of  neat  cement  about  3 
ins.  in   diameter,   H    in.  thick  at  center,   and   tapering  to  a 
thin  edge  shall  be  kept  in  moist  air  for  a  period  of  twenty- 
four  hours. 

(a)  A  pat  is  then  kept  in  air  at  normal  temperature  and 
observed  at  intervals  for  at  least  28  days. 

(b)  Another  pat  is  kept  in  water  maintained  as  near 
70°  F.  as  practicable,  and  observed  at  intervals  for  at  least 
28  days. 

(c)  A  third  pat  is  exposed  in  any  convenient  way  in 
an  atmosphere  of  steam,  above  boiling  water,  in   a  loosely 
closed  vessel  for  five  hours. 


SPECIF  1C  A  TIONS.  419 

(24)  These  pats,  to   satisfactorily  pass  the  requirements, 
shall  remain  firm  and  hard  and  show  no  signs  of  distortion, 
checking,  cracking  or  disintegrating. 

(25)  Sulphuric  Acid  and  Magnesia. — The  cement  shall  not 
contain  more  than  1.75  per  cent  of  anhydrous  sulphuric  acid 
(SO3),  nor  more  than  4  per  cent  of  magnesia  (MgO). 

UNIFORM  TESTS  OF  CEMENT. 

(Condensed  from  methods  recommended  by  the  committee 
on  uniform  tests  of  cement  of  the  Am.  Soc.  of  C.  E.) 

Sampling. — The  sample  shall  be  a  fair  average  of  the  con- 
tents of  the  package;  it  is  recommended  that  where  condi- 
tions permit  one  barrel  in  every  ten  be  sampled. 

All  samples  should  be  passed  through  a  sieve  having 
twenty  meshes  per  linear  inch,  in  order  to  break  up  lumps 
and  remove  foreign  material;  this  is  also  a  very  effective 
method  for  mixing  them  together  in  order  to  obtain  ,an 
average.  For  determining  the  characteristics  of  a  shipment 
of  cement  the  individual  samples  may  be  mixed  and  the 
average  tested;  where  time  will  permit,  however,  it  is  recom- 
mended that  they  be  tested  separately. 

Cement  in  barrels  should  be  sampled  through  a  hole 
made  in  the  center  of  the  staves,  midway  between  the  heads 
or  in  the  head  by  means  of  an  auger  or  a  sampling  iron 
similar  to  that  used  by  sugar  inspectors.  If  in  bags  it 
should  be  taken  from  surface  to  center. 

Chemical  Analysis. — The  method  proposed  by  the  com- 
mittee on  Uniformity  in  the  Analysis  of  Materials  for  the 
Portland  Cement  Industry,  of  New  York  Section  of  the 
Society  for  Chemical  Industry,  should  be  used  as  published 
in  the  journal  of  the  society  for  January  15,  1902. 

Specific  Gravity. — The  determination  of  specific  gravity 
should  be  made  with  Le  Chatelier's  apparatus,  and  benzine 
(62°  Baume  naphtha)  and  kerosene  free  from  water  should  be 
used  in  making  the  determination.  The  specific  gravity  is  the 
weight  of  the  cement  divided  by  the  displaced  volume. 

Fineness. — Fineness  is  determined  on  circular  sieves  about 
7.87  ins.  in  diameter  2.36  ins.  high  and  provided  with  a  pan 


420  REINFORCED    CONCRETE. 

1.97  ins.  deep  and  a  cover,  and  provided  with  a  woven  wire 
cloth   from   brass   wire   having  the  following   diameters: 
No.  100,  0.0045  ins.;  No.  200,  0.0024  ins. 
No.  100  should  have  96  to  100  meshes  to  the  linear  inch. 
No.  200  should  have  188  to  200  meshes  to  the  linear  inch. 

Normal  Consistency. — This  is  best  determined  by  Vicat 
needle  apparatus,  a  description  of  which  may  be  found  in  any 
of  the  treatises  of  cement  or  reinforced  concrete. 

Standard  Sand. — The  Sandusky  Portland  Cement  Com- 
pany of  Ohio  will  furnish  on  application  prepared  sand  from 
Ottawa,  111.,  at  the  price  only  sufficient  to  cover  the  actual 
cost  of  preparation. 

Form  of  briquette  and  molds  to  be  for  samples  1  in.  square 
and  3  ins.  long  of  the  form  illustrated  in  all  text  books. 

Mixing. — Proportions  by  weight,  the  metric  system,  an 
average  temperature  of  21°  C.,.  dry  sand,  cement  mixed  on 
plate  glass  and  hand  kneading  are  required,  and  the  molds 
should  be  filled  at  once,  the  material  being  pressed  in  firmly 
with  the  fingers  and  smoothed  out  with  a  trowel  without 
ramming. 

Storage  of  the  Test  Pieces. — Moist  air  for  24  hours  and 
then  immersed  in  water  as  near  21°  C.  as  possible. 

Tensile  Strength. — Tests  to  be  made  on  a  standard  ma- 
chine without  cushioning  the  points  and  immediately  after 
removing  the  test  pieces  from  the  water. 

Constancy  of  Volume. — Pats  to  be  2.95  ins.  in  diameter, 
0.49  in.  thick  in  center  and  tapering  to  a  thin  edge  are  sub- 
mitted to  a  normal  test  and  an  accelerated  test.  The  first, 
after  immersion  in  water  for  28  days,  the  other  exposed  in 
an  atmosphere  of  steam.  To  pass  these  tests  satisfactorily, 
the  pats  should  remain  firm  and  hard  and  show  no  signs  of 
cracking,  distortion  or  disintegration. 

Miscellaneous  Information. — To  determine  the  quantity 
of  materials  required  for  a  known  mixture  of  concrete: 

Example. — Materials  required  for  1,000  cu.  yds.  of  1-2-4 
concrete: 


SPECIFIC  A  TIONS.  421 

1  bbl.  cement  3.8  cu.  ft.,  sand  30  per  cent  voids,  stone  45  per 
cent  voids. 

1  bbl.  cement    3.8  cu.  ft 3.80  cu.  ft. 

2  bbls.  sand       7.6  cu.  ft.,  30  per  cent  voids 5.32  cu.  ft. 

4  bbls.  stone    15.2  cu.  ft,  45  per  cent  voids 8.36  cu.  ft. 

Loose  material  26.6  cu  ft in  place 17.48  cu.  ft. 

1  bbl.  cement  produces  17.48  cu.  ft.  concrete. 

GLOSSARY  OF  TERMS  USED  IN  PLAIN  AND  REIN- 
FORCED  CONCRETE. 

Accelerated  Test. — A  test  generally  made  to  determine 
soundness  of  a  cement,  hastened  by  subjecting  the  test 
specimen  to  heat,  sometimes  dry  heat,  sometimes  hot 
or  boiling  water.  Such  tests  are  determined  by  hours, 
while  long  time  tests  require  days,  months  or  even  years. 

Activity. — Relating  to  the  rate  of  hardening  of  cement. 

Aggregate. — The  sand  and  gravel  or  crushed  stone  combined 
with  cement  in  the  formation  of  concrete. 

Armored   Concrete. — See   Reinforced   Concrete. 

Bag  of  Cement. — Weighs  95  Ibs.  or  is  equivalent  to  one- 
fourth  of  a  barrel. 

Ball  Mills. — Circular  drums  used  in  cement  manufacture, 
grinding  clinkers  or  stone  between  circumference  of  the 
rotating  drums  and  forged  steel  balls  contained  in  same. 

Barrel  cf  Cement. — Weighs  380  Ibs.  net,  contains  four  bags 
of  cement. 

Batch. — The  definite  quantity  of  concrete  made  at  one  mix- 
ing. 

Beton. — The  French  term  for  concrete. 

Beton  Arme. — The   French  term  for  reinforced  concrete. 

Blowing. — Effect  of  air  bubbles  on  finished  surface,  due  to 
overwet  mixtures  not  properly  stirred  or  tamped. 

Bond,  Mechanical. — See  Mechanical  Bond. 

Bonding.— The  uniting  of  one  layer  or  course  of  concrete 
with  another. 


422  REINFORCED    CONCRETE. 

Briquet'te. — A  small  brick  of  cement  paste,  mortar,  or  con- 
crete having  a  definite  area  at  the  smallest  section  and 
made  for  testing  purposes. 

Bush-hammered. — A  method  of  dressing  stone,  applicable  to 
concrete,  produced  by  dressing  with  a  hammer  having 
large  point-like  teeth  on  the  striking  face. 

Carrying  Rods. — Term  used  to  designate  those  rods  which 
carry  or  sustain  the  load;  they  extend  lengthwise  in  the 
reinforced  member. 

Cement. — A  preparation  of  calcined  clay  and  limestone  or 
their  equivalents  possessing  the  property  of  hardening 
into  a  solid  mass  when  moistened  with  water. 

Cement  Mortar.- — Mortar  composed  of  cement,  sand  and 
water. 

Cement  Sampler.— A  small  tool  used  to  take  a  sample  of 
cement  from  a  barrel,  for  testhig  purposes. 

Centering. — A  wooden  form  giving  shape  to  a  concrete  arch 
while  setting. 

Centers. — Same  as  Centering. 

Checks.- — Same  as  hair  cracks. 

Cinder  Concrete. — Concrete  in  which  cinders  are  used  as 
one  of  the  aggregates. 

Concrete. — A  compact  mass  of  broken  stone,  gravel  or  other 
suitable  material  mixed  together  with  cement  mortar  and 
allowed  to  harden. 

Concrete  Steel. — See  Reinforced  Concrete. 

Construction  Joint.' — The  seam  between  two  successive  days' 
work  in  concrete  laying. 

Corrugated  Bar. — A  form  of  reinforcing  steel,  made  by  press- 
ing the  surface  of  a  plain  bar  into  a  series  of  ridges  or 
corrugations. 

Craze. — Same  as  hair  cracks — generally  the  result  of  too  rich 
a  mixture — occasionally  a  sign  of  unsound  cement. 

Crusher  Run. — -Crushed  stone  taken  directly  from  the  crushei 
with  none  of  the  fine  material  screened  out. 


GLOSSARY.  423 

Distributing  Rods. — Term  used  to  designate  those  rods  which 
distribute  the  load  over  the  carrying  rods;  they  extend 
crosswise  in  the  reinforced  member. 

Dressing. — The  finish  given  to  the  surface  of  concrete. 

Dry  Mix  or  Dry  Mixture. — A  concrete  mixed  with  so  little 
water  that  very  hard  ramming  is  required  to  show  moist- 
ure on  the  surface. 

Early  Stage. — The  first  part  of  the  chemical  action  cement 
mortar  undergoes  after  mixing,  such  as  initial  set  and 
final  set,  both  of  which  precede  hardening. 

Efflorescence. — A  white  discoloration  appearing  on  the  sur- 
face of  concrete,  due  to  the  leaching  out  of  soluble  salts. 

Expanded  Metal. — A  form  of  reinforcing  material,  made  by 
cutting  sheet  steel  in  a  series  of  short  parallel  rows,  and 
drawing  the  sheet  to  form  diamond-shaped  meshes. 

Expansion  Crack. — Cracking  in  concrete  work  caused  by  ex- 
pansion. 

Expansion  Joint. — A  vertical  joint  or  opening  between  two 
masses  of  concrete  to  allow  for  variations  due  to  changes 
of  temperature. 

Fabric,  Wire.— See  Wire  Fabric. 

Facing. — A  rich  mortar  placed  on  exposed  surfaces  to  pro- 
duce a  smooth  finish. 

Falsework. — Wooden  or  other  supports  for  holding  concrete 
in  position  while  setting. 

Ferro-cement. — See  Reinforced  Concrete. 

Ferro-concrete. — See  Reinforced  Concrete. 

Final  Set. — Is  reached  when  a  paste,  mortar  or  concrete  will 
support  a  pressure  of  the  thumb  without  indenting — an 
arbitrary  period  of  setting  of  concrete  just  preceding 
hardening. 

Fineness  of  Cement. — Is  the  degree  of  pulverization,  and  for 
either  cement  or  sand  is  measured  in  terms  of  the  num- 
bers of  the  two  sieves  between  which  it  is  held. 

Finishing. — Working  the  concrete  or  mortar  surface  with 
steel  trowels  or  similar  tools,  as  for  instance  by  brush, 
called  brush  finish. 


424  REINFORCED  CONCRETE. 

Fireproofing. — Method  of  protecting  structural  parts  that  are 
subject  to  damage  by  fire,  by  covering  them  with  a 
material  that  is  not  affected  by  high  temperature,  for 
instance  reinforced  concrete. 

Floating. — Preparing  the  roughly  spread  mortar  for  the  steel 
trowel  by  the  use  of  a  wooden  or  cork  float.  If  this 
floating  is  used  for  a  finish,  it  is  called  float-finish. 

Flush. — To  bring  water  to  the  surface  of  concrete  by  com- 
pacting or  ramming. 

Forms. — Wooden  or  other  molds  to  give  concrete  the  de- 
sired shape  until  hardened, 

Gaging. — Determining  the  proportions  of  cement,  sand, 
gravel  or  broken  stone  and  water  in  concrete.  Generally 
used  in  specifying  the  quantity  of  water  that  will  produce 
a  certain  consistency. 

Granolithic. — Concrete  in  which  the  stone  aggregate  is  very 
finely  crushed;  its  most  general  use  being  as  a  top  sur- 
face for  concrete  walks. 

Grappiers  Cement. — A  French  cement  made  by  grinding  hard, 
under-burned  nodules  which  have  escaped  disintegration 
in  the  manufacture  of  hydraulic  limes. 

Gravel. — Mixture  of  coarse  rounded  pebbles  and  sand,  or 
pebbles  without  sand. 

Grout. — A  thin  mortar  composed  of  sand,  cement  and  water; 
either  poured  or  applied  with  a  brush. 

Hair  Cracks. — Fine  hair-like  cracks  on  the  surface  of  a  ce- 
ment or  concrete  structure  which  has  stood  for  some 
time. 

Hardening. — Commences  after  the  final  set  of  a  cement, 
mortar  or  concrete  and  continues  for  a  number  of  years. 

High  Carbon  Steel. — A  steel  in  which  the  elastic  limit  is  not 
less  than  52,500  Ibs.  per  sq.  inch. 

Hinge  Joints. — Joints  which  divide  a  structure  into  several 
sections,  each  one  of  which  can  expand  independent  of 
the  others. 

Hooped  Concrete. — Concrete  columns  reinforced  with  wires 
wound  spirally  or  placed  in  annular  rings. 


•GLOSSARY.  425 

Hydrated  Lime. — Made  by  mixing  quicklime  and  water;  the 
chemical  formula  is  CaO  +  H2O  =  CaOzH* 

Hydraulic  Cement. — Any  cement  which  sets  or  hardens  un- 
der water. 

Initial  Set. — Takes  place  when  a  mass  of  cement  begins  to 
solidify;  is  defined  by  the  length  of  time  required,  vary- 
ing according  to  the  kind  of  cement  under  test. 

Kahn  Bar. — A  form  of  reinforcement  named  after  the  inven- 
tor, consisting  of  a  special  rolled  section  of  steel  with 
diagonal  members  sheared  directly  from  the  sides  of  the 
bar  and  bent  upward. 

Kiln. — A  stationary  or  rotary  furnace  used  in  cement  manu- 
facture. 

Laitance. — Pulpy,  gelatinous  fluid  washed  from  cement  that 
is  deposited  in  water. 

Lean  Mixture. — A  concrete  containing  a  relatively  small 
proportion  of  cement. 

Limestone. — An  aggregate  for  concrete,  consisting  largely 
of  CaO,  CO2,  and  SiO2. 

Loam. — Earth  or  vegetable  mold  composed  largely  or  en- 
tirely of  organic  matter. 

Matrix. — A  term  sometimes  used  for  Mortar. 

Mechanical  Bond. — Increased  adhesion  due  to  deformations 
in  reinforcing  material. 

Mix. — A  shortened  term  for  Mixture. 

Mixer. — A  machine  for  mechanically  mixing  concrete. 

Mixture  or  Mix. — Refers  either  to  the  proportions  of  mate- 
rials composing  concrete  or  to  its  consistency. 

Molds. — Wooden  or  other  forms  used  to  hold  concrete  in 
the  desired  shape  until  hardened. 

Monolithic. — Built  in  one   solid,  continuous   piece. 

Mortar,  Cement. — A  mixture  of  cement,  sand  and  water.  Very 
finely  crushed  stone  may  be  used  in  place  of  the  sand. 

Natural  Cement. — The  finely  pulverized  product  resulting 
from  the  calcination  of  an  argillaceous  limestone  at  a 
temperature  only  sufficient  to  drive  off  the  carbonic  acid 
gas. 


426  REINFORCED  CONCRETE. 

Neat  Cement. — Or  cement  paste,  is  cement  mixed  with  water 
without  the  addition  of  any  aggregate. 

Paste,  Cement. — A  mixture  of  cement  and  water. 

Pat. — A  small  quantity  of  neat  cement  spread  upon  glass  for 
testing  purposes. 

Pointing. — Filling  in  joints  or  depressions  on  the  face  of 
concrete. 

Portland  Cement. — The  finely  pulverized  product  resulting 
from  the  calcination  to  incipient  fusion  of  an  intimate 
mixture  of  properly  proportioned  argillaceous  and  cal- 
careous materials  and  to  which  no  addition  greater  than 
3  per  cent  has  been  made  subsequent  to  calcination. 

Puddling. — The  mechanical  or  hand  stirring  of  wet  concrete 
in  the  mold  when  too  wet  to  be  tamped  or  rammed. 

Pozzolan. — Same  as  Puzzolan. 

Puzzolan. — An  intimate  mixture  made  by  grinding  together 
granulated  furnace  slag  and  slaked  lime  without  further 
calcination,  possessing  the  hydraulic  qualities  of  cement. 

Quaking  Concrete. — Concrete  mixed  with  that  proportion  of 
water  which  will  cause  it  to  quake  like  jelly  when  heavily 
tamped. 

Quick  Setting. — Term  applied  to  cement  which  takes  an  ini- 
tial set  in  a  comparatively  short  time;  is  an  arbitrary 
term. 

Ramming. — Heavy   compacting   of   concrete   with   a   suitable 

tool. 
Regaging. — Adding   water    to  mortar  which  has  become  stiff 

and  working  same  until  plastic. 

Reinforced  Concrete. — Variously  known  as  armored  concrete, 
steel  concrete,  concrete  steel,  etc.,  is  concrete  in  which  is 
embedded  steel  in  such  form  as  to  take  up  the  tension 
and  assist  in  resisting  shear. 

Reinforcement. — The  iron  or  steel  used  in  reinforced  con- 
crete. 

Reinforcing. — Applying  the  reinforcement — also  used  in  the 
same  sense  as  reinforcement. 


GLOSSARY.  427 

Rich  Mixture. — A  concrete  containing  relatively  a  large  pro- 
portion of  cement. 

Roman  Cement. — The  English  term  for  natural  cement 

Rosendale  Cement. — A  natural  cement  from  the  Rosendale 
district  in  eastern  New  York. 

Rotary  Kiln  or  Rotary. — Used  in  cement  manufacture— see 
Kiln. 

Rubble  Concrete. — Concrete  in  which  rubble  stone  are  im- 
bedded. 

Sampler. — See   Cement   Sampler. 

Sand. — Aggregate  of  particles  of  gravel  passing  a  No.  5  sieve 
(having  openings  .16  in.  wide),  the  grains  being  1/16  in. 
in  diameter  or  under. 

Sand  Cement. — Same  as  Silica  Cement. 

Scale. — To  flake  off  in  thin  layers. 

Screenings. — A  fine  aggregate  separated  from  crushed  stone 
and  used  in  the  place  of  sand. 

Set. — Solidification  to  such  a  degree  that  change  of  form  will 
produce  rupture.  In  cement,  set  begins  when  a  Vicat 
needle  0.039  in.  in  diameter  weighing  10.58  oz.  penetrates 
only  .20  in.  into  the  mortar,  and  is  complete  when  the 
needle  will  not  penetrate  at  all.  Approximately,  when 
cement  paste  resists  a  light  pressure  of  the  finger  nail. 

Shrinkage  Cracks. — Due  to  contraction  of  concrete  on  ac- 
count of  temperature  changes. 

Silica  Cement. — Clean  sand  and  Portland  cement  ground 
together. 

Slag  Cement. — Another  name  for  Puzzolan  Cement. 

Sloppy  Concrete. — Concrete  mixed  with  that  proportion  of 
water  which  prevents  it  from  being  piled  up  in  the 
barrow. 

Slow  Setting  Cement. — That  which  requires  two  hours  or 
longer  in  setting.  The  term  is  arbitrary. 

Soundness. — Refers  to  property  of  not  expanding,  contracting 
or  checking  in  setting. 


428  REINFORCED    CONCRETE. 

Standard  Sand. — Recommended  by  the  American  Society  for 
Testing  Materials  is  the  natural  sand  from  Ottawa,  Illi- 
nois, screened  to  pass  a  sieve  having  20  meshes  per  linear 
inch  and  retained  on  a  sieve  having  30  meshes  per  linear 
inch;  the  wires  to  have  diameters  of  0.0165  and  0.0112  ins., 
respectively,  i.  e.,  half  the  width  of  the  opening  in  each 
case.  Sand  having  passed  the  No.  20  sieve  shall  be  con- 
sidered standard  when  not  more  than  1  per  cent  passes  a 
No.  30  sieve  after  one  minute  continuous  sifting  of  a 
500-gram  sample. 

Steel-Concrete. — See  Reinforced  Concrete. 

Tamp.— To  firmly  compact  concrete  with  a  suitable  tool. 

Test. — An  examination  into  the  condition  or  quality  of  a 
cement,  a  concrete  or  its  aggregates. 

Thacher  Bar. — A  deformed  bar  used  in  reinforced  concrete, 
named  after  its  inventor. 

Top  Surface. — The  exposed  horizontal  surface  of  cement  or 
concrete  work;  usually  applied  to  the  finishing  coat  of 
sidewalks. 

Trap  Reck. — A  heavy  rock  which  when  crushed  forms  an 
excellent  aggregate  for  concrete. 

Trowel. — A  steel  tool  used  in  finishing  a  cement  or  concrete 
surface;  also  the  act  of  using  said  tool. 

Tube  Mill. — A  rotary  mill  or  furnace  used  in  the  manufac- 
ture of  cement  in  conjunction  with  ball  mills. 

Twisted  Steel. — Reinforcing  material  made  by  twisting  square 
steel  bars. 

Underburned  Cement. — A  cement  burned  at  too  low  tempera- 
ture; the  clinker  of  such  cement  is  lacking  in  density. 

Vassy  Cement. — The  product  obtained  by  heating  limestone 
containing  much  clay  at  the  lowest  temperature  that  will 
decarbonate  the  lime;  it  sets  very  rapidly  but  hardens 
very  slowly. 

Vicat  Needle. — An  apparatus  containing  a  needle  named  after 
its  inventor,  used  in  testing  cement  pats. 


GLOSSARY.  429 

Voids.— The    spaces   between   the    particles   of    sand,   gravel, 

crushed  stone  or  other  aggregate. 
Wearing  Surface.— Finished  surface  exposed  to  wear. 
Wet   Mix   or  Wet   Mixture.— Concrete    mixed   with   enough 

water  so  that  little  or  no  ramming  is  needed. 
Wire   Fabric.— A    reinforcing   material     composed    of   wires 

crossing  at  right  angles  and  secured  at  the  intersections. 


430  REINFORCED    CONCRETE. 

USEFUL    INFORMATION. 

WEIGHT    OF    STEEL    BRIDGES. 

1.  Weight  of  steel  in  single-track,  I-beam  span,  no  ballast. 

ZF=3.5  Z,2+352£+1215. 

2.  Single-track  deck  plate  girder  span,  no  ballast, 

W=9.5  £2+200£+450  (less  than  70  feet), 
JF=28£2+2280Z: +83400  (more  than  70  feet). 

3.  Single-track  through  plate  girder  span,  no  ballast, 

W=1S24L— 26160  (less  than  76  feet), 

W=  75Z, 2— 2927^+433740  (more  than  76  feet). 

4.  Single-track  through  pin  span,  no  ballast, 

W=  7.9Z,2+870Z, + 1 1500. 

5.  Double-track  through  plate  girder  span    (2  light  and   1 
heavy  girders)  (no  ballast  floor), 

fF=4Z,2+2980Z— 44000  (30-80  feet  span), 
JF=68£2+352800  (80-100  feet  span). 

6.  Double-track    through    pin    span    (2    light    and    1    heavy 
girders)  (no  ballast  floor), 


RAPID  SOLUTION  OF  QUADRATIC  AND  CUBIC 
EQUATIONS,  BY  SUBSTITUTION 

1.     Quadratic  Eq: 

Ex:      3jtr2+18  x  =  48 

6  x  =  16        p  =  6,  q  =  16 


2.     Cubic  Eq: 

f  +  py-g 


USEFUL  INFORMATION. 
If  the  equation  is 

we  make 


431 


-\-  nx 


x  =  y -  and  have 


(3) 


Here 
and 


n  —  ~    is  the  p  of  eq.  (1) 


m   (  2m*  \ 

r g-  ^— 9~   -  «  I  is  the  q  of  eq.  ( 

hereby  we  find  y,  and  from  eq.  (3)  we  find  x. 
(Engineering  and  Contracting,  Jan.  11,  1911.) 


TABLE  LXXXIV.— LIFE  OF  PLANT  m  YEARS. 


Rate  of  Interest  of  Installments,  Per  Cent. 


Depreciation 

of  Plant. 

3% 

4% 

5% 

6% 

8% 

1 

46.90 

41.04 

36.73 

33.40 

28.55 

2 

31.00 

28.01 

25.68 

23.79 

20.91 

3 

23.45 

21.50 

20.10 

18.85 

16.88 

4 

18.93 

17.62 

16.62 

15.73 

14.28 

5 

15.90 

14.99 

14.21 

13.53 

12.42 

6 

13.72 

13.02 

12.42 

11.90 

11.01 

7 

12.05 

11.52 

11.04 

10.62 

9.90 

8 

10.77 

10.34 

9.95 

9.60 

9.01 

9 

9.72 

9.37 

9.05 

8.76 

8.26 

10 

8.88 

8.58 

8.31 

8.07 

7.64 

11 

8.16 

7.91 

7.68 

7.47 

7.10 

12 

7  06 

13 

6.60 

14 

6  30 

15 

5.85 

16 

5  55 

17 

5  33 

18 

5.04 

19 

4  91 

20 

4.56 

432 


REINFORCED    CONCRETE. 


AMORTIZATION. 

R  y=annual  installment 

of  interest 


N 


r>    I     p 

1°8" — ~ —  N=  number  of  years 


Z=°fo  of  depreciation 
TABLE  LXXXV. 


log 


Life  of 
Plant, 
Years. 

5 
6 
7 
8 
9 
10 
11 
12 
13 
14 
15 
16 
17 
18 
19 
20 

Annual  Installments. 

Rate  of  Interest  of  Installments,  Per  Cent. 

3% 

4% 

5% 

6% 

8% 

$  .1810 
.1465 
.1230 
.1050 
.0907 
.0795 
.07039 
.06283 
.06646 
.05103 
.04634 
.04227 
.03870 
.03555 
.03275 
.03024 

$''06903 
.06008 
.05269 
.04652 
.04130 
.03683 
.03298 
.0?963 
.02670 
.02413 
.02185 

$  .08723 
.07808 
.07046 
.06403 
.05853 
.05376 
.04961 
.04595 
.04271 
.03891 
.03722 

$  .08330 
.07416 
.06656 
.06015 
.05467 
.04994 
.04582 
.04220 
.03899 
.03614 
.03058 

$  .07587 
.06679 
.05928 
.05296 
.04759 
.04296 
.02895 
.03544 
.03236 
.02962 
.02718 

INDEX. 


Page 

Accident  insurance 408 

Adhesion,  concrete  to  forms..  197 

concrete  to  steel 76 

Aggregates,    choice   of. 5 

cinders    13 

crushed  stone    11 

graded,  voids  in 13 

gravel    10 

kinds  of 4 

slag    14 

voids  in,  determination  of.     5 

graded   13 

tables  of   6 

Angles,   properties   of 58 

Arch    bridge,     Grand    River, 

Grand   Rapids,    Mich.... 28 9 
Santa  Monica  Viaduct,  Cal- 
ifornia     292 

Arch  centers,  construction  of.  28  6 

examples   of 287 

Grand  River  bridge 292 

Pollasky   bridge    287 

removing,    time  and  meth- 
ods   of 289 

Santa  Monica  viaduct 293 

Arch  construction,   centers. .  .286 
classification  of  arches.  .  .  .286 

concreting  arch  ring 288 

Arch  design,  assumptions.  .  .  .275 

constructing  arch  ring 275 

dead  load  diagram 277 

elastic  theory  simplified.  .  .252 
example      of,      by      elastic 

theory    275 

live  load  diagram 279 

maximum  fiber   stresses. .  .281 

Area,  of  circles 64 

of  round   rods 31 

of  steel  reinforcement. .  .33-35 

Beams,  bending  moments  for.  69 
calculation,    numerical    ex- 
ample     168 

designing,  table  for 140 

formulas    for    ultimate 

strength   of 140 

Pittsburgh    Steel    Products 

Go's 51 

reinforcement  for,  Colgnet.126 

Coularou    126 

frame   systems 127 

Hennebique   125 

Locher   126 

loose  rod 125 


Page 
Beams  (Continued). 

safe  load  and  steel  area 
tables  127 

stirrups,   location  of... 74,  170 

tests  of  tee-beams 77 

Bending  moments',   beams...   69 

slabs 120 

maximum  in    120 

table  for 71 

Bins,  grain  flowing  from.... 3 70 

bridging  action  of  grain  in.370 

capacity  of 379 

cement  storage,  Illinois 
Steel  Co 382 

design   of 370 

diagram  of  wheat  pressure 
in 373 

friction  of  grain  on  con- 
crete   375 

lateral  and  vertical  pres- 
sures, ratio  between.  ..  .375 

pressure  of  coal  in .'376 

pressure  of  grain  in,  Ketch- 
urn's  conclusions 380 

tables  of 370 

ratio  of  grain  to  liquid 
pressure  372 

vertical  pressure  in 374 

Bridges',    arch,     classification 
of 246 

classification,   by  loadings. 211 
general    211 

design  and  construction  of.  211 

diagrams  for  loadings.  212,  213 

flat  slab,  detailed  designs 
of 216-221 

flat  slab  and  girder,  gen- 
eral discussion 211 

formulas   for    arches.  .246-251 

girder,       detailed       design 

of    221-229 

designs       complete       for 
spans  of  20  to   40   ft, 

tables   for 238-240 

standard    designs,    table 

loadings,  class  1 233 

class  2 234 

class  3 235 

Impact,  diagram  illustrat- 
ing   215 

live  loads,  data  for  weights 
and  dimensions  of  elec- 
tric cars 216 


433 


434 


INDEX. 


Page 
Bridges  (Continued) 

distribution    of 214 

method  of  finding  wheel 
loads  on  roadway,  dia- 
gram illustrating 214 

on  track 215 

Building    construction,    clear- 
ing the  site. ...  . 183 

concreting  columns 186 

in  freezing  weather 189 

walls    187 

delivering  concrete. ......  .186 

depositing    concrete 186 

eliminating    forms    in 201 

finishing  concrete  surfaces.204 

forms    and    falsework 189 

kind  of  lumber 190 

making  the  concrete 185 

ordering  materials 184 

placing   reinforcement 184 

safe    loads    for    spruce    or 

pine  beams,  table 190 

safe  loads  for  wooden  pil- 
lars,  table 191 

separately  molded  members 

for 200 

sequence  of  operations.  ..  .183 

small  tools  for 202 

Building  design,    adhesion   of 

concrete  to  steel 76 

assumptions  made  in.. 67,   167 

beams     .  .168 

beams  and  girders 125 

beams,    bending  moments..    69 

bracket   connections 165 

columns    144 

dead  loads,  assumptions  for     68 

elasticity,   modulus  of 77 

example   of  warehouse. ..  .167 

floors    94 

foundations   78 

live  loads,  assumptions  for.   69 
percentage      of      reinforce- 
ment       68 

roofs   160 

slabs,  bending  moments  for.    71 

stairs    . 160 

steel  or  cast  iron  columns.  161 
stirrups,      location     of,      in 

beams 74 

stresses,   allowable   in   con- 
crete       69 

Cement,  barrel  of,  volume...  2 

weight    2 

color  of 4 

fineness    3 

magnesia  in,  allowable.  ...  3 

packages  for  shipment....  1 

Portland,  definition  of 1 


)  Page 

Cement  (Continued). 

setting,  thumb  nail  test  for     4 

time  of 3 

specifications  for 2,   416 

specific   gravity 3 

storage,  requirements  for.  .      2 

strength,    tensile 3 

sulphuric  a£id  in,  allowable     3 

testing,  necessity  of 3 

samples,   method  of  tak- 
ing          4 

test   requirements   for 3 

volume,    constancy   of 3 

Channels,   properties   of 56 

Chimneys,   calculation   of.... 390 
approximate    method.  ..  .392 

core  theory 391 

design      of,      summary      of 

points    in 395 

horse  power  of 327 

forms,    construction   of.  ...398 

steel    concrete 396 

Wiederholt   construction.  .  .398 
wind  pressure  and  velocity.392 
Cinders,   choice  and  use  of .  .    13 
Circles,  areas  and  circumfer- 
ences   of 64 

Columns,    calculation   of,    nu- 
merical  example 172 

cast    iron 161 

classification    of 147 

concreting,  method  of 186 

crushing      strength,      Kim- 
ball's  tests,   table 145 

diagram  showing  average 

unit   stress,   Lindau 146 

Talbot's  tests,   table 145 

Euler's    formula    for 159 

full-sized    specimens, 

tests    146 

hooped,   calculation  of 149 

Considered   formula  for.  156 

forms   of r.  .  .  149 

tables  for  designing 150 

rectangular,    calculation . .  .147 

forms   of 147 

spiral,  Talbot's  tests  of...  158 

structural    steel 161 

table    for   wire    spirals.  ..  .156 
Concrete,      adhesion     of,     to 

forms    197 

to    steel 76 

consistency,    proper 24 

definition    of 17 

depositing  in  building  con- 
struction     186 

finishes    for,    see    Concrete 

finishes. 

hair  cracks  in,  eliminating.205 
joining  new  to  old 188 


INDEX. 


435 


Page 
Concrete    (Continued). 

mixing,  hand  or  machine.  .    24 

requirements   of 21 

mixtures,  plain  concrete.  .  .    22 

reinforced   concrete 22 

wet  vs.   dry 21 

proportioning,  Fuller's  rule 

for    20 

maximum   density 20 

strength     18 

methods  of 17 

Thacher's  tables  for 19 

proportions      for     different 

classes    of   work 21 

protection  from  freezing. .  .189 

while    setting 188 

sand  for,   best 8 

small   tools  for 202 

specifications   for 411 

stresses  in,  allowable 69 

transporting      in      building 

construction    186 

Concrete  carts 203 

Concrete    finishes,    dry    mix- 
tures for 206 

mortar    facing 205 

painting   and    varnishing.  .207 

plastering    207 

scrubbed  and  acid  work. ..206 

tooling   207 

types  of 205 

Concrete  mixers,  batch,  clas- 
sification   of 24 

sizes  and  capacities 26 

batch    or   continuous 24 

continuous,  classification  of  27 

sizes   and  capacities 28 

gravity,    Hains 28 

Concrete,    reinforced,    defini- 
tion   of 1 

names  for,  various' 1 

Conduits,    calculations,    char- 
acter   of 335 

cast  pipe,  stresses,  concen- 
trated load 339 

distributed    vertical 

load    340 

Talbot's   tests 339 

tests  on,  summary  of... 342 
thickness  and  weight  of. 338 
external     pressure,     calcu- 
lation   for 336 

flow  of  water  in  circular.  .334 
internal    pressure,    calcula- 
tion   for .  .335 

Myer's  formula 336 

Rankine's  rule 337 

sewer,   grades  in 335 

reinforcement  for 337 


Page 
Conduits    (Continued). 

soil,    resistance    to    erosion 

by  water 332 

Talbot's    formula 337 

velocity   of  water  in,   Che- 

zy's   formula   for 333 

Kutter's  formula  for.  .  .  .333 
water,    erosive    and    trans- 
porting power  of 332 

Connections,  examples  of.  . .  .165 
Corrugated  bars,  weight  and 

area        38 

Cost  keeping,  methods  of . . .  .400 

Costs,   conc_ete  culverts 324 

tanks    361 

timber  and   concrete   grain 

elevators    382 

timber  and  concrete  piles.    84 
Crus-hed  stone,   choice  of. ...    11 

crusher    run 12 

size  of 11 

voids  in,  table  of 14 

Culvert  and  sewer  pipe, 
table  thickness  and 
weight  of  reinforcement 

for    339 

Culverts,  arch,   design  of.... 320 

Great  Northern  Ry 329 

Kalamazoo,    Mich 328 

standard,  C.,   B.  &  Q.  Ry.  .327 
Culverts,     box,     assumptions 

for .320 

covers,  design  of 320 

diagram   for  design   of.. 3 21 

sides,   design   of 323 

diagram  for  design   of.. 323 

standard,  C.,  B.  &  Q.  Ry..  .331 

Culverts1,  cost  of 324 

Dams,   classification  of 347 

construction,  types  of 352 

curtain    type 355 

half  apron  type 355 

open  front  type 354 

pressures       on       immersed 

surface 350 

stresses  in,  comparison  of 
gravity  and  pressure 
dams1  347 

Decimals,  feet,  inches  and 
fractions  64 

Designing  methods,  Lindau, 
tables  for  beams  and  slabs 
141,  142,  143 

Elastic  theory  of  arches.  ...  252 
critical  condition  of  loading 

for  given   section 260 

line  of  pressure  for 256 

from  dead  load 256 


436 


INDEX. 


Page 

Elastic  Theory  (Continued), 
reactions   from   concentrat- 
ed   load 253 

successive  steps  in  arch  de- 
sign   256 

thermal   stresses 274 

thickness   of  arch  ring 267 

Elasticity,   modulus  of 77 

Estimating,    suggestions    for.  405 

Finishes     for     concrete,     see 
Concrete  finishes. 

Floors,   arch,   forms  of 101 

Monier    101 

Roebling    101 

Wuensch    101 

beam  and  tile 100 

beam,  forms  of 99 

classification    of 95 

Heidenreich    flat    slab    sys- 
tem  106 

loads',    specified 94 

manufactured,    Siegwart. . .  102 

Visintini    102 

"mushroom"   system 103 

safety,  factor  of 95 

slab,    calculation  of 106 

Columbian 96 

Cottancin 97 

expanded   metal 96 

forms   of 97 

Matrai    95 

Monier    96 

Roebling    97 

umbrella  flat  slab  system.  104 
Forms,   adhesion  of  concrete.197 

alignment  of 196 

chimneys   398 

column*,  example  of 199 

combined     steel     and    con- 
crete   construction 199 

design   of 193 

fastening,  methods  of 194 

grain   elevator 388 

joints  in 194 

lagging,  thickness  of 196 

lumber  for,  kinds  of 190 

railing  for  bridge 291 

removing,  time  for 197 

removing    312 

setting    310 

rotation  in  use  of 196 

studs,  for  spacing  of 196 

tank    368 

Formulas,  Cain's,  for  retain- 
ing walls 297 

beams  reinforced  for  com- 
pression     113 

Chezy's,  for  flow  of  water.333 
columns     .  .  .115 


Page 

Formulas    (Continued). 

Considered  for  hooped  col- 
umns     149 

Euler's,   for  columns 159 

for   beams 70,     71 

ultimate   strength   of 104 

for  deflection 194 

for  hooped  columns 149 

for    parabola 275 

for  strength  of  mortar.  ...    15 

for  wind   pressure 79 

Johnson's,   for   temperature 

cracks    299 

Kutter's,     for    velocity    of 

water   333 

parabolic   line    118 

Rankine's,      for      retaining 

walls     297 

rectangular   beams 108 

shear  bond  and  arch  rein- 
forcement      114 

straight   line 108 

rectangular  beams Ill 

tee  beams Ill 

Foundations,     concrete     pile, 

see   Piles,   concrete, 
concrete  pile,   types  of.  ...    79 

loads    on 79 

mat     92 

portable   92 

raft,  calculation  of,  numer- 
ical  example 172 

for  warehouse 90 

slab,   kinds   of 83 

types  of,  for  buildings 78 

Girders,   see   Beams. 

Glossary  of  terms  used 421 

Grain,    action    of,    in    flowing 

from  bins 370 

bridging  action  of 370 

pressures,  table  of 370 

Grain      elevators,      Canadian 
Pacific,  Port  Arthur,  Ont.386 

classification    of 381 

forms     for     Port     Arthur, 

Ont.,    elevator 388 

Heidenreich 389 

timber  and  concrete,   com- 
parative  cost 382 

Gravel,  characteristics  of. ...    10 

Hair       cracks,       eliminating, 

methods  of 205 

Hinges,    parabolic    arch   with 
two    .  ..248 

I-beams,  properties  of.... 56,  57 
Inertia,  moment  of,  for  vari- 
ous sections 66 


INDEX. 


437 


Page 

Inspection,   necessity   of 399 

Leaks,   stopping  leaky  floors.209 
Loads,      dead,      assumed     in 

building   design 68 

floor,   specified 94 

live,    assumed    in    building 
design 69 

Oakum,  for  waterproofing. .  .209 

Manufactured    articles 399 

Measuring  box 203 

Mixers  (see  Concrete  mixers). 

Modulus   of   elasticity 77 

of    sections 66 

Moment  of  inertia  of  sections  66 

Mortar,  definition  of 15 

retempered    16 

sand  for,  best 7 

strength  of,  conditions  gov- 
erning        15 

tests,   of,   value  of 16 

volume     of,     with     varying 

proportions  of  sand 16 

weight    of 16 

Oakum,   for  waterproofing. . .  209 

Painting    concrete 207 

Piles,    concrete,    Chenoweth. .   88 

corrugated    87 

cost     of,     compared     with 

wood 84 

driving,  methods  of 88 

Pedestal 87 

Raymond 80 

Simplex    85 

types   of 79 

unpatented  forms 88 

Plastering    concrete 207 

Profits,    percentage    to    allow 

for    407 

Protection    of    steel    in    con- 
crete      209 

by    Tockolith 209 

Rammers,  cast  iron 203 

wood    204 

Reinforcement,  against  shear     73 
American  hooped    column...    54 

American  wire  fabric 46 

angles,  properties  of 58 

channels,  properties  of .  .56,   57 

Coignet  for  beams 126 

Colling's    corrugated    bars, 

tests  of 40,  41 

Columbian  for  floors 96 

column     J 1  f> 

compression    113 

corrugated     bars,     weights 
and  areas  of 37 


Page 

Reinforcement    (Continued), 
table  of  spacing  for  given 

area    124 

Cottancin    for    floors 97 

Coularou  for  beams 126 

Cummings  girder  frame...  50 
Cummings  hooped  column.  53 
cup  bars,  weights  and  sizes 

of 40 

diamond  bars,  weights  and 

areas  of 38 

expanded    metal 48 

flats,  areas  of 33,   34 

weights  of 33,  34 

frame  sy stems  for  beams.  127 
Heidenreich    flat    slab    sys- 
tem,  floor  and  column..  106 
Hennebique,  for  beams.  . .  .125 

hooped  column 53 

I-beams,   properties  of.. 56,   57 

Kahn   rib   metal 48 

Kahn  trussed  bar. .  . 51 

Locher  for  beams 126 

lock  woven  fabric 46 

loose  rods   for 35 

Luten    truss.. 53 

Matrai,  for  floors 97 

mechanical    bond 32 

Monier,   for  floors 96 

"Mushroom"    system 103 

percentage    of 31,   68 

placing,     in     building    con- 
struction     184 

rods,   areas   of  square   and 

round   31 

weights    of    square    and 

round   31 

Roebling  for  floors 97 

round   rods   for 35 

spacing  for  given  area..  123 
weight  for  given  spacing.  123 
sections,  properties  of  vari- 
ous        66 

Smith  hooped  column 54 

square    bars,    table,    areas 

of    124 

square  rods  for 35 

steel,   adhesion  of  concrete 

to    76 

high  vs.  low  carbon 39 

medium    30 

strength    of 29 

steel   woven   wire,    triangle 

mesh    43 

structural   steel 55 

styles   of 33 

T-beams    115 

Thacher  bars,  weights  and 

areas    39 

triangle  mesh,  tables  of.44,  45 


438 


INDEX. 


Page 

Reinforcement  (Continued), 
twisted   bars,    weights   and 

areas    35 

"umbrella"    flat    slab    sys- 
tem,  floor   and   column..  10 4 

"Unit"    frame 51 

units  beam  and  girder....   50 

welded  wire  fabric 47 

wire,  standard  gages 42 

Xpantrus   bar 51 

Reservoirs1,  see  Tanks. 
Retaining    wall    design,    ma- 
sonry,  example   of 300 

reinforced     concrete     beam 

type,    example   of 303 

Retaining   walls,    backfilling. 299 

Cain's   formulas 298 

expansion  joints 299,  312 

Great  Northern   Ry 314 

masonry,   crushing  of,   sta- 
bility   against 302 

overturning,    stability 

against 301 

resultant  pressure,  calcu- 
lation  of 301 

sliding,  stability  against. 3 01 

Paris'  Exposition,    1900 313 

Retaining  Walls    (Continued), 
pressures  on,  Cain's  theory.297 

Coulomb's  theory 297 

Rankine's  theory 296 

Trautwine's   theory 297 

Weyrauch's  theory 296 

Rankine's  formulas  for 297 

reinforced    concrete,    beam 

type,    foundation 304 

vertical    beam 303 

with   counterforts 309 

foundations     310 

pressure,  calculation  of.307 

vertical    slab 308 

specifications  for 317 

temperature  cracks. 299 

thrust   299 

R.  I.  W.  for   putty 180 

for  waterproofing 180 

Rock  crushers,  capacity  of .  .    12 
gyratory,   sizes  and  capac- 
ity      13 

Round  rods,  table  of  spacing 

for  given  area 123 

table  of  weights  for  given 

spacing    123 

Roofs,    forms   of 160 

Sand    (see    also    Screenings). 

Sand,  cleanness,  requirements 

for    8 

concrete,   best   for 8 

definition    of 6 


Page 
Sand  (Continued). 

mortar,  best  for 7 

selection   of 6 

standard,   definition  of 10 

voids  in,  conditions  govern- 
ing          9 

table    of 9 

theory   of 9 

washing,   method  of 8 

weight    of 10 

Santa  Monica  viaduct 292 

for    putty 180 

Screenings',  characteristics  re- 
quired        10 

Section   modulus 66 

Sections,    properties   of 66 

Sewers,  see  Conduits. 

Shearing  provisions 73 

Slabs,   bending  moments   for.   70 

maximum    120 

calculation,   notation   used.  106 
parabolic   line   formula..  118 
straight   line   formula.  .  .108 
designing,  table  for.  .  .142,  143 
thickness      and      reinforce- 
ment,  table   showing..  122 

Slag,    aeration   of 14 

Soils,   bearing  power  of 79 

Specifications,     Portland    ce- 
ment    417 

reinforced      concrete      con- 
struction     411 

retaining  wall  construction. 3 17 
Square  bars,  table  areas  of.  124 
Stairs,  kinds  of,  construction.  160 
Stirrups',  location  of,  in 

beams 74,  69 

Stresses,     allowable    In    con- 
crete     170 

Tanks,     American     Steel     & 

Wire    Co 368 

calculation   of 358 

capacity,   table  of 359 

cost    of 361 

foundations    for 358 

general    discussion 357 

intake,   forms  for 368 

Montgomery   Ward  &   Co.  .361 

shapes    of 357 

tightness    of 360 

Tee-beams,    design    of,    table 

for 116,    117,    118 

tests  of 77 

Tie  for  wall  forms 312 

Timber,   strength   of 191 

Tockolith 209 

Tooling  concrete 207 

Tools1,      small      for     concrete 
work   .  .  .  202 


INDEX. 


439 


Toxement 


Page 

.  .210 


Useful     information 430 

quadratic   and    cubic   equa- 
tions, rapid  solution  of.. 430 
plant,   life  of  in   years.... 430 
amortization     430 

Voids,  in  graded  mixtures. . .  13 

in  loose  broken  stone 13 

in    sand 9 

table    of 5 

Walls,  concreting,  methods 
of  187 

Water,  erosive  and  trans- 
porting power 332 


Page 

Waterproofing,  directions  for. 2 07 
cracked  walks  or  joints... 209 

necessity   of 208 

protection  of  steel  in  con- 
crete      209 

toxement 210 

Weight    of    brick    walls  per 

superficial    foot 95 

Weights  of  various  sub- 
stances stored  in  ware- 
houses    94 

Wheelbarrows    203 

Wind  pressures,  table  of 393 

Wire  gage,   area  of  wire  for 
1   ft.  in  width 42 

Xpantrus    bar 61 


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